Spatial Ecology via Reaction‐Diffusion Equations

DOI10.1002/0470871296zbMath1059.92051OpenAlexW2481427767MaRDI QIDQ4443621

Chris Cosner, Robert Stephen Cantrell

Publication date: 18 January 2004

Full work available at URL: https://doi.org/10.1002/0470871296

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Ecology (92D40) Research exposition (monographs, survey articles) pertaining to biology (92-02)

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II: Different diffusion and advection rates ⋮ Ecological release and patch geometry can cause nonlinear density-area relationships ⋮ Impact of population size and movement on the persistence of a two-strain infectious disease ⋮ An age-space structured cholera model linking within- and between-host dynamics with Neumann boundary condition ⋮ On a uniqueness of solution for a reaction-diffusion type system with a free boundary ⋮ Biological invasion in a predator-prey model with a free boundary ⋮ Density-dependent effects on Turing patterns and steady state bifurcation in a Beddington-DeAngelis-type predator-prey model ⋮ A time-periodic reaction-diffusion population model of a species subjected to harvesting on the boundary of a protected habitat ⋮ Asymptotic dynamics of a logistic SIS epidemic reaction-diffusion model with nonlinear incidence rate ⋮ A monotone iteration for a nonlinear Euler-Bernoulli beam equation with indefinite weight and Neumann boundary conditions ⋮ Global dynamics and asymptotic profiles for a degenerate dengue fever model in heterogeneous environment ⋮ The diffusive Lotka-Volterra competition model in fragmented patches. I: Coexistence ⋮ A modified techniques of fractional-order Cauchy-reaction diffusion equation via Shehu transform ⋮ Spatio-temporal dynamic solitary wave solutions and diffusion effects to the nonlinear diffusive predator-prey system and the diffusion-reaction equations ⋮ Classification of the spreading behaviors of a two-species diffusion-competition system with free boundaries ⋮ Global dynamics of a diffusive competition model with habitat degradation ⋮ Propagation dynamics for an age-structured population model in time-space periodic habitat ⋮ Predator invasion in predator-prey model with prey-taxis in spatially heterogeneous environment ⋮ The logistic equation with nonlinear advection term ⋮ Global dynamics of a general competitive reaction-diffusion-advection system in one dimensional environments ⋮ Dynamics of a nonautonomous predator--prey system with the Beddington-DeAngelis functional response ⋮ Evolution of a semilinear parabolic system for migration and selection in population genetics ⋮ Pattern formation in a cross-diffusive ratio-dependent predator-prey model ⋮ Competition of three species in an advective environment ⋮ Complex dynamics of a reaction-diffusion epidemic model ⋮ On logistic models with a carrying capacity dependent diffusion: stability of equilibria and coexistence with a regularly diffusing population ⋮ Spreading speed, traveling waves, and minimal domain size in impulsive reaction-diffusion models ⋮ Persistence and extinction in spatial models with a carrying capacity driven diffusion and harvesting ⋮ On a free boundary problem for a two-species weak competition system ⋮ Pattern formation in a cross-diffusive Holling-Tanner model ⋮ How flow speed alters competitive outcome in advective environments ⋮ Evolution of passive movement in advective environments: general boundary condition ⋮ Spreading fronts in a partially degenerate integro-differential reaction-diffusion system ⋮ Spatiotemporal patterns of a homogeneous diffusive predator-prey system with Holling type III functional response ⋮ Quenching phenomenon for a parabolic MEMS equation ⋮ Single species models with logistic growth and dissymmetric impulse dispersal ⋮ An SIS epidemic reaction-diffusion model with spontaneous infection in a spatially heterogeneous environment ⋮ Phase transitions in a logistic metapopulation model with nonlocal interactions ⋮ Dynamics of a diffusion reaction prey-predator model with delay in prey: effects of delay and spatial components ⋮ Global stability and pattern formation in a nonlocal diffusive Lotka-Volterra competition model ⋮ Free boundary models for mosquito range movement driven by climate warming ⋮ Existence and asymptotic of traveling wave fronts for the delayed Volterra-type cooperative system with spatial diffusion ⋮ A double \(S\)-shaped bifurcation curve for a reaction-diffusion model with nonlinear boundary conditions ⋮ Strong competition model with non-uniform dispersal in a heterogeneous environment ⋮ The spreading speed for a predator-prey model with one predator and two preys ⋮ Spatiotemporal pattern formation and selection induced by nonlinear cross-diffusion in a toxic-phytoplankton-zooplankton model with Allee effect ⋮ A time-periodic diffusive prey-predator model with sign-changing growth rates and a free boundary ⋮ A reaction-diffusion-advection model for Aedes aegypti mosquitoes in a time-periodic environment ⋮ On a Lotka-Volterra type competition model from river ecology ⋮ Influence of diffusion on the stability of a full Brusselator model ⋮ The role of protection zone on species spreading governed by a reaction-diffusion model with strong Allee effect ⋮ Stability and convergence of radial basis function finite difference method for the numerical solution of the reaction-diffusion equations ⋮ Stability and traveling waves of a vaccination model with nonlinear incidence ⋮ Coexistence of a cross-diffusive dengue fever model in a heterogeneous environment ⋮ Traveling waves for \(n\)-species competitive system with nonlocal dispersals and delays ⋮ Analysis of positive solutions for a class of semipositone \(p\)-Laplacian problems with nonlinear boundary conditions ⋮ Unilateral global bifurcation for a class of quasilinear elliptic systems and applications ⋮ A heterogeneous parasitic-mutualistic model of mistletoes and birds on a periodically evolving domain ⋮ Local dynamics and coexistence of predator-prey model with directional dispersal of predator ⋮ Global behavior of a multi-group SEIR epidemic model with age structure and spatial diffusion ⋮ Modeling the effects of trait-mediated dispersal on coexistence of mutualists ⋮ On the interplay of harvesting and various diffusion strategies for spatially heterogeneous populations ⋮ Global dynamics of a Lotka-Volterra competition-diffusion-advection system for small diffusion rates in heterogenous environment ⋮ Spatiotemporal dynamics and spatial pattern in a diffusive intraguild predation model with delay effect ⋮ Persistence and spread of stage-structured populations in heterogeneous landscapes ⋮ Dynamics of a consumer-resource reaction-diffusion model. Homogeneous versus heterogeneous environments ⋮ Coexistence in a competition-diffusion-advection system with equal amount of total resources ⋮ Fractional generalized logistic equations with indefinite weight: quantitative and geometric properties ⋮ Stability of synchronized steady state solution of diffusive Lotka-Volterra predator-prey model ⋮ A weak competition system with advection and free boundaries ⋮ Global dynamics of a Lotka-Volterra competition-diffusion system in advective homogeneous environments ⋮ Existence and stability of coexistence states for a reaction-diffusion-advection model ⋮ Lipschitz stability for the growth rate coefficients in a nonlinear Fisher-KPP equation ⋮ Global dynamics of a classical Lotka-Volterra competition-diffusion-advection system ⋮ Numerical solutions of equations of cardiac wave propagation based on Chebyshev multidomain pseudospectral methods ⋮ A time-periodic dengue fever model in a heterogeneous environment ⋮ Turing patterns in a reaction-diffusion system modeling hunting cooperation ⋮ Hopf bifurcation and pattern formation in a delayed diffusive logistic model with spatial heterogeneity ⋮ Cosymmetry approach and mathematical modeling of species coexistence in a heterogeneous habitat ⋮ A two-species weak competition system of reaction-diffusion-advection with double free boundaries ⋮ The effects of simple density-dependent prey diffusion and refuge in a predator-prey system ⋮ Extinction and coexistence of species for a diffusive intraguild predation model with B-D functional response ⋮ Coexistence and extinction in time-periodic Volterra-Lotka type systems with nonlocal dispersal ⋮ On a free boundary problem for a nonlocal reaction-diffusion model ⋮ Invasion and coexistence of competition-diffusion-advection system with heterogeneous vs homogeneous resources ⋮ Theoretical analysis on a diffusive SIR epidemic model with nonlinear incidence in a heterogeneous environment ⋮ A weighted networked SIRS epidemic model ⋮ Long-time behavior of the solutions of Murray-Thomas model for interacting chemicals ⋮ Hopf and steady state bifurcation analysis in a ratio-dependent predator-prey model ⋮ On the periodic Ambrosetti-Prodi problem for a class of ODEs with nonlinearities indefinite in sign ⋮ Steady-state bifurcation and Hopf bifurcation for a diffusive Leslie-Gower predator-prey model ⋮ Effects of patch-matrix composition and individual movement response on population persistence at the patch level ⋮ Reaction-diffusion models: from particle systems to SDE's ⋮ Strong continuity of eigen-pairs of the Schrödinger operator with integrable potentials ⋮ Multidimensional control systems: case studies in design and evaluation ⋮ Convergence in competition models with small diffusion coefficients ⋮ Global dynamics of a competition model with non-local dispersal. I: The shadow system ⋮ On principal eigenvalues of measure differential equations and a patchy Neumann eigenvalue problem ⋮ The stability and Hopf bifurcation of the diffusive Nicholson's blowflies model in spatially heterogeneous environment ⋮ Existence and stability of steady-state solutions of reaction-diffusion equations with nonlocal delay effect ⋮ Turing instability in pioneer/climax species interactions ⋮ Bifurcation and stability of a two-species reaction-diffusion-advection competition model ⋮ Mathematical analysis of an age-structured HIV/AIDS epidemic model with HAART and spatial diffusion ⋮ Theoretical analysis for a PDE-ODE system related to a glioblastoma tumor with vasculature ⋮ Analysis of a malaria epidemic model with age structure and spatial diffusion ⋮ The effect of temporal variability on persistence conditions in rivers ⋮ Ecological and evolutionary dynamics in advective environments: critical domain size and boundary conditions ⋮ Existence and stability of patterns in a reaction-diffusion-ODE system with hysteresis in non-uniform media ⋮ The noise and the KISS in the cancer stem cells niche ⋮ Analysis of a degenerate reaction-diffusion host-pathogen model with general incidence rate ⋮ Dynamics for a two-species competitive Keller-Segel chemotaxis system with a free boundary ⋮ The optimal distribution of resources and rate of migration maximizing the population size in logistic model with identical migration ⋮ Asymptotic profiles of the endemic equilibrium of a reaction-diffusion-advection SIS epidemic model with saturated incidence rate ⋮ On the unboundedness of the ratio of species and resources for the diffusive logistic equation ⋮ Qualitative analysis of a Lotka-Volterra competition-diffusion-advection system ⋮ Effect of diffusion in a spatial SIS epidemic model with spontaneous infection ⋮ Classification of global dynamics of competition models with nonlocal dispersals. I: Symmetric kernels ⋮ Interaction between prey and mutually interfering predator in prey reserve habitat: pattern formation and the Turing-Hopf bifurcation ⋮ Tracking prey or tracking the prey's resource? Mechanisms of movement and optimal habitat selection by predators ⋮ Dynamics of a diffusive competition model in spatially heterogeneous environment ⋮ Positive steady states of reaction-diffusion-advection competition models in periodic environment ⋮ On the importance of dimensionality of space in models of space-mediated population persistence ⋮ Establishing a beachhead: a stochastic population model with an Allee effect applied to species invasion ⋮ Dynamical complexity of a spatial phytoplankton-zooplankton model with an alternative prey and refuge effect ⋮ A spatial SIS model in advective heterogeneous environments ⋮ Propagation of CaMKII translocation waves in heterogeneous spiny dendrites ⋮ A SIS reaction-diffusion model with a free boundary condition and nonhomogeneous coefficients ⋮ Spreading-vanishing dichotomy in information diffusion in online social networks with intervention ⋮ Evolutionarily stable dispersal strategies in a two-patch advective environment ⋮ Long-time dynamics of an SIRS reaction-diffusion epidemic model ⋮ A reaction-diffusion-advection free boundary problem for a two-species competition system ⋮ Global wellposedness for a class of reaction-advection-anisotropic-diffusion systems ⋮ Optimal control of growth coefficient on a steady-state population model ⋮ Bifurcation scenario of Turing patterns in prey-predator model with nonlocal consumption in the prey dynamics ⋮ On Lotka-Volterra competitive parabolic systems: exclusion, coexistence and bistability ⋮ Pattern formation in a reaction-diffusion-ODE model with hysteresis in spatially heterogeneous environments ⋮ Dynamics in a delayed competition system on a weighted network ⋮ Analysis of a two-strain malaria transmission model with spatial heterogeneity and vector-bias ⋮ Spatial versus non-spatial dynamics for diffusive Lotka-Volterra competing species models ⋮ Stability of Dirac concentrations in an integro-PDE model for evolution of dispersal ⋮ Hopf bifurcation in a reaction-diffusion equation with distributed delay and Dirichlet boundary condition ⋮ Evolution of anisotropic diffusion in two-dimensional heterogeneous environments ⋮ Concentration profile of endemic equilibrium of a reaction-diffusion-advection SIS epidemic model ⋮ Study on monostable and bistable reaction-diffusion equations by iteration of travelling wave maps ⋮ Sharp estimates for the spreading speeds of the Lotka-Volterra diffusion system with strong competition ⋮ A reaction-diffusion model of harmful algae and zooplankton in an ecosystem ⋮ Qualitative analysis on an SIRS reaction-diffusion epidemic model with saturation infection mechanism ⋮ On a nonlinear nonlocal model for a population with separate dispersal and sedentary stages ⋮ Spatial-temporal dynamics of a diffusive Lotka-Volterra competition model with a shifting habitat II: Case of faster diffuser being a weaker competitor ⋮ Prey-predator dynamics with prey refuge providing additional food to predator ⋮ On the effect of lowering population's movement to control the spread of an infectious disease ⋮ Spreading speeds for the predator-prey system with nonlocal dispersal ⋮ Qualitative analysis of a diffusive SEIR epidemic model with linear external source and asymptomatic infection in heterogeneous environment ⋮ Concentration phenomenon of the endemic equilibrium of a reaction-diffusion-advection SIS epidemic model with spontaneous infection ⋮ Qualitative analysis of a Lotka-Volterra predator-prey system with migration ⋮ The effect of advection on a predator-prey model in open advective environments ⋮ Another mechanism to control invasive species and population explosion: ``ecological damping continued ⋮ Scalable uncertainty quantification for deep operator networks using randomized priors ⋮ Bounded positive solutions for diffusive logistic equations with unbounded distributed limitations ⋮ On the fitness of predators with prey-induced dispersal in a habitat with spatial heterogeneity ⋮ Mathematical study of a resource-based diffusion model with Gilpin-Ayala growth and harvesting ⋮ Bifurcation analysis of a Kolmogorov type tritrophic model ⋮ Stationary and non-stationary pattern formation over fragmented habitat ⋮ Persistence and extinction of population in reaction-diffusion-advection model with strong Allee effect growth ⋮ Intraguild predation with evolutionary dispersal in a spatially heterogeneous environment ⋮ Population dynamics with resource-dependent dispersal: single- and two-species models ⋮ Dynamics of a predator-stage structured model with cannibalism, degenerate diffusion and free boundaries ⋮ On positive solutions for a class of quasilinear elliptic equations ⋮ Analysis of integrodifference equations with a separable dispersal kernel ⋮ Basic reproduction ratio of a mosquito-borne disease in heterogeneous environment ⋮ Effects of dispersal rates in a two-stage reaction-diffusion system ⋮ Attractors and long transients in a spatio-temporal slow-fast Bazykin's model ⋮ Impact of travel between patches for spatial spread of disease ⋮ Density dependent behavior at habitat boundaries and the Allee effect ⋮ Global dynamics of a Lotka-Volterra competition-diffusion system with nonlinear boundary conditions ⋮ Modeling epidemic flow with fluid dynamics ⋮ A free boundary problem for a ratio-dependent predator-prey system ⋮ The Lotka-Volterra models with non-local reaction terms ⋮ The bang-bang property in some parabolic bilinear optimal control problems \textit{via} two-scale asymptotic expansions ⋮ Evolution of dispersal in advective patchy environments ⋮ Qualitative analysis on a reaction-diffusion nutrient-phytoplankton model with toxic effect of Holling-type II functional ⋮ Analysis on a diffusive SIRS epidemic model with logistic source and saturated incidence rate ⋮ Dynamics of a reaction-diffusion-advection model with two species competing in a flow reactor ⋮ Dynamics of a diffusive competition model with memory effect and spatial heterogeneity ⋮ Range limits in spatially explicit models of quantitative traits ⋮ Spatiotemporal dynamics in epidemic models with Lévy flights: a fractional diffusion approach ⋮ Dynamic behavior of a reaction-diffusion dengue model with spatial heterogeneity ⋮ On the ratio of total masses of species to resources for a logistic equation with Dirichlet boundary condition ⋮ The diffusive logistic model with a free boundary in heterogeneous environment ⋮ Perceptive movement of susceptible individuals with memory ⋮ Open problems in PDE models for knowledge-based animal movement via nonlocal perception and cognitive mapping ⋮ Spatio-temporal solutions of a diffusive directed dynamics model with harvesting ⋮ Dynamics of additional food provided predator-prey system with mutually interfering predators ⋮ Mean occupancy time: linking mechanistic movement models, population dynamics and landscape ecology to population persistence ⋮ Asymptotic profile of the positive steady state for an SIS epidemic reaction-diffusion model: effects of epidemic risk and population movement ⋮ Solving the density classification problem with a large diffusion and small amplification cellular automaton ⋮ Evolution of dispersal toward fitness ⋮ The spreading front of invasive species in favorable habitat or unfavorable habitat ⋮ Positive solutions of a diffusive Leslie-Gower predator-prey model with Bazykin functional response ⋮ Normal forms for semilinear equations with non-dense domain with applications to age structured models ⋮ Global bifurcation and nodal solutions for fourth-order problems with sign-changing weight ⋮ Stationary solutions in a closed distributed Eigen-Schuster evolution system ⋮ Species persistence decreases with habitat fragmentation: an analysis in periodic stochastic environments ⋮ A diffusive competition model with a protection zone ⋮ Boundedness and large-time behavior results for a diffusive epidemic model ⋮ Mathematical analysis of the optimal habitat configurations for species persistence ⋮ Application of He's variational iteration method for solving the Cauchy reaction-diffusion problem ⋮ On the effects of migration and spatial heterogeneity on single and multiple species ⋮ Environmentally induced dispersal under heterogeneous logistic growth ⋮ Bifurcation diagrams of population models with nonlinear diffusion ⋮ Persistence in reaction diffusion models with weak Allee effect ⋮ The Speed of Epidemic Waves in a One-Dimensional Lattice of SIR Models ⋮ $R_0$ Analysis of a Benthic-Drift Model for a Stream Population ⋮ Asymptotic behavior of solutions of Fisher-KPP equation with free boundary conditions ⋮ A free boundary problem of a predator-prey model with higher dimension and heterogeneous environment ⋮ Spreading and vanishing behaviors for radially symmetric solutions of free boundary problems for reaction-diffusion equations ⋮ Internal null stabilization for some diffusive models of population dynamics ⋮ Success, failure, and spreading speeds for invasions on spatial gradients ⋮ Traveling wavefronts in nonlocal dispersal and cooperative Lotka-Volterra system with delays ⋮ A dynamic model for the ideal-free distribution as a partial differential equation ⋮ On a Competition-Diffusion-Advection System from River Ecology: Mathematical Analysis and Numerical Study ⋮ Global dynamics of a Lotka-Volterra type prey–predator model with diffusion and predator-taxis ⋮ Selected Topics on Reaction-Diffusion-Advection Models from Spatial Ecology ⋮ Allee effect and bistability in a spatially heterogeneous predator-prey model ⋮ ON THE RATIO OF BIOMASS TO TOTAL CARRYING CAPACITY IN HIGH DIMENSIONS ⋮ Persistence for stochastic difference equations: a mini-review ⋮ Global bifurcation of the nondifferentiable Sturm-Liouville problems with indefinite weight and spectral parameter in the boundary condition ⋮ Dynamical response of a reaction–diffusion predator–prey system with cooperative hunting and prey refuge ⋮ Spots, traps, and patches: asymptotic analysis of localized solutions to some linear and nonlinear diffusive systems ⋮ An $hp$-adaptive Newton-discontinuous-Galerkin finite element approach for semilinear elliptic boundary value problems ⋮ Spatial dynamics of a nonlocal model with periodic delay and competition ⋮ Dynamics of an infection age-space structured cholera model with Neumann boundary condition ⋮ Evolution of cross-diffusion and self-diffusion ⋮ How Does Nonlocal Dispersal Affect the Selection and Stability of Periodic Traveling Waves? ⋮ A New Monotonicity for Principal Eigenvalues with Applications to Time-Periodic Patch Models ⋮ Deciphering Dynamics of Epidemic Spread: The Case of Influenza Virus ⋮ DYNAMICS OF A DIFFUSIVE PREDATOR–PREY MODEL WITH ADDITIVE ALLEE EFFECT ⋮ Dynamical behaviors of a diffusive predator–prey system with Beddington–DeAngelis functional response ⋮ Two-phase problem with a free boundary for systems of parabolic equations with a nonlinear term of convection ⋮ Two Novel proofs of Spectral Monotonicity of Perturbed Essentially Nonnegative Matrices with Applications in Population Dynamics ⋮ A PREDATOR–PREY INTERACTION MODEL WITH SELF- AND CROSS-DIFFUSION IN AQUATIC SYSTEMS ⋮ An indefinite nonlinear problem in population dynamics: high multiplicity of positive solutions ⋮ On the Conjecture of the Role of Advection in a Two-Species Competition-Diffusion Model ⋮ Local and Global Existence for Nonlocal Multispecies Advection-Diffusion Models ⋮ A DIFFUSIVE LOGISTIC EQUATION WITH MEMORY IN BESSEL POTENTIAL SPACES ⋮ Time Dependent Diffusion as a Mean Field Counterpart of Lévy Type Random Walk ⋮ A reaction–diffusion SIS epidemic model with saturated incidence rate and logistic source ⋮ Bifurcation analysis of coexistent state in a delayed two-species predator-prey model ⋮ On a reaction–advection–diffusion equation with Robin and free boundary conditions ⋮ On Impulsive Reaction-Diffusion Models in Higher Dimensions ⋮ Prey-predator model with a nonlocal consumption of prey ⋮ Existence and Stability of Stationary States of a Reaction–Diffusion-Advection Model for Two Competing Species ⋮ Patterns in a Modified Leslie–Gower Model with Beddington–DeAngelis Functional Response and Nonlocal Prey Competition ⋮ Exploring Complex Dynamics of Spatial Predator–Prey System: Role of Predator Interference and Additional Food ⋮ On a Smale theorem and nonhomogeneous equilibria in cooperative systems ⋮ Study of a Mixed Dispersal Population Dynamics Model ⋮ Unnamed Item ⋮ The importance of census times in discrete-time growth-dispersal models ⋮ Pattern Formation Scenario through Turing Instability in Interacting Reaction Diffusion Systems with Both Refuge and Nonlinear Harvesting ⋮ On the Basic Reproduction Number of Reaction-Diffusion Epidemic Models ⋮ Spatiotemporal Dynamics Induced by Michaelis–Menten Type Prey Harvesting in a Diffusive Leslie–Gower Predator–Prey Model ⋮ Coexistence states in a cross-diffusion system of a predator–prey model with predator satiation term ⋮ Dynamics and pattern formation of a diffusive predator–prey model with predator-taxis ⋮ Monotonicity and Global Dynamics of a Nonlocal Two-Species Phytoplankton Model ⋮ Wave propagation for a class of non-local dispersal non-cooperative systems ⋮ The Numerical Analysis of the Long Time Asymptotic Behavior for Lotka-Volterra Competition Model with Diffusion ⋮ Homogenization techniques for population dynamics in strongly heterogeneous landscapes ⋮ Dynamics of populations with individual variation in dispersal on bounded domains ⋮ Delay-driven pattern formation in a reaction–diffusion predator–prey model incorporating a prey refuge ⋮ Spatiotemporal dynamics in a reaction–diffusion toxic-phytoplankton–zooplankton model ⋮ MONOTONE METHODS AND STABILITY RESULTS FOR NONLOCAL REACTION-DIFFUSION EQUATIONS WITH TIME DELAY ⋮ A Wolbachia infection model with free boundary ⋮ On several conjectures from evolution of dispersal ⋮ Evolutionary stability of ideal free nonlocal dispersal ⋮ Analytical and numerical approaches to coexistence of strains in a two-strain SIS model with diffusion ⋮ Propagation of Turing patterns in a plankton model ⋮ Pest persistence and eradication conditions in a deterministic model for sterile insect release ⋮ Evolution of dispersal in closed advective environments ⋮ A Fragmentation Phenomenon for a Nonenergetic Optimal Control Problem: Optimization of the Total Population Size in Logistic Diffusive Models ⋮ EXACT AND APPROXIMATE TRAVELING WAVES OF REACTION-DIFFUSION SYSTEMS VIA A VARIATIONAL APPROACH ⋮ Effects of impulsive harvesting and an evolving domain in a diffusive logistic model* ⋮ Unnamed Item ⋮ Global Dynamics of a Lotka--Volterra Competition-Diffusion System in Advective Heterogeneous Environments ⋮ Feedback Stabilization for a Reaction-Diffusion System with Nonlocal Reaction Term ⋮ Minimum wave speeds in monostable reaction–diffusion equations: sharp bounds by polynomial optimization ⋮ Bifurcation in nonlinear Sturm-Liouville problems with indefinite weight and spectral parameter in the boundary condition ⋮ The transmission of dengue virus with Aedes aegypti mosquito in a heterogeneous environment ⋮ Scaling Limits for Some P.D.E. Systems with Random Initial Conditions ⋮ Anisotropic diffusion in oriented environments can lead to singularity formation ⋮ Classification of radial solutions arising in the study of thermal structures with thermal equilibrium or no flux at the boundary ⋮ Dynamics of a diffusive competitive model on a periodically evolving domain ⋮ The Emergence of Range Limits in Advective Environments ⋮ On the steady solutions of fractional reaction-diffusion equations ⋮ Global Dynamics of the Lotka-Volterra Competition-Diffusion System: Diffusion and Spatial Heterogeneity I ⋮ Optimization results for the higher eigenvalues of the p‐Laplacian associated with sign‐changing capacitary measures ⋮ Steady-State Problem of an S-K-T Competition Model with Spatially Degenerate Coefficients ⋮ Some Novel Results in Two Species Competition ⋮ Patterns and Transitions to Instability in an Intraspecific Competition Model with Nonlocal Diffusion and Interaction ⋮ Spreading Speeds and Linear Determinacy for Two Species Competition Systems with Nonlocal Dispersal in Periodic Habitats ⋮ GLOBAL DYNAMICS OF A POPULATION MODEL FROM RIVER ECOLOGY ⋮ On existence, multiplicity, uniqueness and stability of positive solutions of a Leslie–Gower type diffusive predator–prey system ⋮ Asymptotics of the Principal Eigenvalue for a Linear Time-Periodic Parabolic Operator I: Large Advection ⋮ Diffusive and nondiffusive population models ⋮ A Hybrid Parabolic and Hyperbolic Equation Model for a Population with Separate Dispersal and Stationary Stages: Well-Posedness and Population Persistence ⋮ The spreading fronts in a mutualistic model with delay ⋮ OPTIMAL HARVESTING OF A SPATIALLY EXPLICIT FISHERY MODEL ⋮ The diffusive model for West Nile virus with advection and expanding fronts in a heterogeneous environment ⋮ The Effect of Directed Movement on the Strong Allee Effect ⋮ Stability and Hopf bifurcation analysis in a Lotka–Volterra competition–diffusion–advection model with time delay effect ^* ⋮ Modelling and Analysis of Predation System with Nonlocal and Nonsingular Operator ⋮ Bifurcation analysis of a single species reaction-diffusion model with nonlocal delay ⋮ SINGULARLY PERTURBED ELLIPTIC SYSTEM MODELING THE COMPETITIVE INTERACTIONS FOR A SINGLE RESOURCE ⋮ Adaptive Local Minimax Galerkin Methods for Variational Problems ⋮ Unnamed Item ⋮ ASYMPTOTIC BEHAVIOR FOR RADIALLY SYMMETRIC SOLUTIONS OF A LOGISTIC EQUATION WITH A FREE BOUNDARY ⋮ Asymptotic Behavior of the Basic Reproduction Ratio for Periodic Reaction-Diffusion Systems ⋮ Reaction-Subdiffusion Equations with Species-Dependent Movement ⋮ On a power-type coupled system of k-Hessian equations ⋮ A Spatiotemporal Model for the Effects of Toxicants on Populations in a Polluted River ⋮ A COMPARATIVE STUDY OF SEMI-ANALYTICAL METHODS FOR SOLVING FRACTIONAL-ORDER CAUCHY REACTION–DIFFUSION EQUATION ⋮ Global dynamics of a Lotka-Volterra competition-diffusion-advection model with stage structure ⋮ Spreading speeds and traveling waves for monotone systems of impulsive reaction-diffusion equations: application to tree-grass interactions in fire-prone savannas ⋮ Dynamical Behavior of a Lotka-Volterra Competitive System From River Ecology ⋮ Threshold dynamics of an age-space structure vector-borne disease model with multiple transmission pathways ⋮ Diffusive spatial movement with memory in an advective environment ⋮ Stability and bifurcation in a reaction-diffusion model with nonlinear boundary conditions ⋮ Effects of environmental heterogeneity on species spreading via numerical analysis of some free boundary models ⋮ Dynamics of a diffusive mussel-algae system in closed advective environments ⋮ Mathematical analysis of the dynamics of some reaction-diffusion models for infectious diseases ⋮ Threshold dynamics of a cooperation–diffusion–advection model in open advective environments ⋮ Spontaneous infection and periodic evolving of domain in a diffusive SIS epidemic model ⋮ Dynamics of an EIS spatially heterogeneous rabies model ⋮ Nonconstant steady states in a predator-prey system with density-dependent motility ⋮ Global analysis on an age‐space structured vaccination model with Neumann boundary condition ⋮ Dynamical behavior of a Lotka–Volterra competition system in open advective environments ⋮ Dynamics of a reaction-diffusion epidemic model with general incidence and protection awareness for multi-transmission pathways ⋮ Turing pattern formation in reaction-cross-diffusion systems with a bilayer geometry ⋮ Dynamics of Lotka-Volterra competition patch models in streams with two branches ⋮ On the role of advection in a spatial epidemic model with general boundary conditions ⋮ Stability and Hopf bifurcation of a heterogeneous diffusive model with spatial memory ⋮ Stable transition layer for the Allen–Cahn equation when the spatial inhomogeneity vanishes on a nonsmooth hypersurface in ℝⁿ ⋮ Evolution of Dispersal in Advective Homogeneous Environments: Inflow Versus Outflow ⋮ Predator-induced prey dispersal can cause hump-shaped density-area relationships in prey populations ⋮ Stability and bifurcation in a single species with nonlinear boundary conditions ⋮ Unnamed Item ⋮ On a principle of predatory exclusion ⋮ Stability and bifurcation of a reaction-diffusion-advection model with nonlinear boundary condition ⋮ Dynamics and calculation of the basic reproduction number for a nonlocal dispersal epidemic model with air pollution ⋮ Global existence and spatiotemporal pattern formation of a nutrient-microorganism model with nutrient-taxis in the sediment ⋮ A diffusion-advection predator-prey model with a protection zone ⋮ The problem of diffusion wave initiation for a nonlinear second-order parabolic system ⋮ Dynamics of a diffusion-advection Lotka-Volterra competition model with stage structure in a spatially heterogeneous environment ⋮ Asymptotic behavior of solutions for multi-stable equation with Dirichlet boundary condition ⋮ Qualitative analysis of a stock-effort parabolic model incorporating marine reserve ⋮ Impact of resource distributions on the competition of species in stream environment ⋮ Multiple positive steady states of a diffusive predator‐prey model in spatially heterogeneous environments ⋮ A free boundary problem for a predator-prey system ⋮ Asymptotic analysis for a nonlinear reaction-diffusion system modeling an infectious disease ⋮ Dynamical behavior of solutions of a reaction-diffusion model in river network ⋮ Spatiotemporal patterns in a diffusive predator–prey system with nonlocal intraspecific prey competition ⋮ Dynamics of a periodic-parabolic Lotka-Volterra competition-diffusion system in heterogeneous environments ⋮ A dengue fever model with free boundary incorporating the time‐periodicity and spatial‐heterogeneity ⋮ Dynamical behavior of a temporally discrete non-local reaction-diffusion equation on bounded domain ⋮ Dynamics of a Leslie-Gower predator-prey model with advection and free boundaries ⋮ Small order limit of fractional Dirichlet sublinear-type problems ⋮ Dynamical behavior of a spatiotemporal model in open advective environments ⋮ Dynamics of the nonlocal diffusive vector-disease model with delay and spatial heterogeneity ⋮ Dynamical analysis of an age-space structured malaria epidemic model ⋮ 1D logistic reaction and \(p\)-Laplacian diffusion as \(p\) goes to one ⋮ Epidemic dynamics and spatial segregation driven by cognitive diffusion and nonlinear incidence ⋮ Coexistence and competitive exclusion in a time-periodic Lotka-Volterra competition-diffusion system ⋮ Propagation phenomena with nonlocal diffusion in presence of an obstacle ⋮ Enhancing population persistence by a protection zone in a reaction-diffusion model with strong Allee effect ⋮ Steady states of a diffusive Lotka-Volterra system with fear effects ⋮ Optimization of total population in logistic model with nonlocal dispersals and heterogeneous environments ⋮ Spatio-temporal dynamics of a reaction-diffusion-advection food-limited system with nonlocal delayed competition and Dirichlet boundary condition ⋮ Steady states of a diffusive predator-prey model with prey-taxis and fear effect ⋮ The asymptotic behavior of bacterial and viral diseases model on a growing domain ⋮ Agro-Ecological Control of a Pest-Host System: Preventing Spreading ⋮ Approximate analytical solution of the generalized Kolmogorov-Petrovsky-Piskunov equation with cubic nonlinearity ⋮ Sharp profiles for diffusive logistic equation with spatial heterogeneity ⋮ Stable discontinuous stationary solutions to reaction-diffusion-ODE systems ⋮ Spatial dynamics of a nonlocal dispersal Leslie-Gower predator-prey model with some shifting habitats ⋮ Human mobility and disease prevalence ⋮ Effects of spatial heterogeneity and homogeneity on an S-K-T competition model ⋮ Spatial heterogeneity localizes Turing patterns in reaction-cross-diffusion systems ⋮ Asymptotic profiles of the steady state for a diffusive SIS epidemic model with Dirichlet boundary conditions ⋮ Dynamics analysis of a reaction-diffusion malaria model accounting for asymptomatic carriers ⋮ Bifurcation analysis on a river population model with varying boundary conditions ⋮ Cross-Diffusion Induced Turing Instability and Amplitude Equation for a Toxic-Phytoplankton–Zooplankton Model with Nonmonotonic Functional Response ⋮ Global threshold dynamics of an infection age-space structured HIV infection model with Neumann boundary condition ⋮ Hopf bifurcation in a reaction-diffusion-advection two species model with nonlocal delay effect ⋮ On a New Type of Chemotaxis Model with Acceleration ⋮ Dynamics of consumer-resource reaction-diffusion models: single and multiple consumer species ⋮ Singular Analysis of the Optimizers of the Principal Eigenvalue in Indefinite Weighted Neumann Problems ⋮ Effects of B-D functional response and protection zone on a predator-prey model ⋮ Dynamical analysis of a competition‐diffusion‐advection system with Dirichlet boundary conditions ⋮ Stationary and oscillatory patterns of a food chain model with diffusion and predator‐taxis ⋮ A single consumer model with Neumann boundary condition ⋮ A return-to-home model with commuting people and workers ⋮ A Diffusive Predator-Prey Model with Spatially Heterogeneous Carrying Capacity ⋮ Global bifurcation results for some fourth‐order nonlinear eigenvalue problem with a spectral parameter in the boundary condition ⋮ Concentration phenomenon of single phytoplankton species with changing-sign advection term ⋮ Analysis on a Spatial SIS Epidemic Model with Saturated Incidence Function in Advective Environments: I. Conserved Total Population ⋮ The principal Floquet bundle and the dynamics of fast diffusing communities ⋮ Positive almost periodic solutions of nonautonomous evolution equations and application to Lotka–Volterra systems ⋮ On cognitive epidemic models: spatial segregation versus nonpharmaceutical interventions ⋮ Logistic elliptic equation with a nonlinear boundary condition arising from coastal fishery harvesting. II ⋮ Existence of forced waves and their asymptotics for Leslie-Gower prey-predator model with some shifting environments ⋮ On the effects of density-dependent emigration on ecological models with logistic and weak Allee type growth terms ⋮ Effects of diffusion and advection on predator-prey dynamics in closed environments ⋮ Resource allocation in a PDE ecosystem model ⋮ Spatio-temporal dynamics of an age-space structured cholera model with bacterial hyperinfectivity and imperfect vaccination ⋮ Complex dynamics of diffusive predator–prey system with Beddington–DeAngelis functional response: The role of prey-taxis ⋮ LSV-Based Tail Inequalities for Sums of Random Matrices ⋮ A Nonstationary Statistical Model for Computationally Intensive Numerical Ordinary Differential Systems ⋮ Dynamics of Lotka-Volterra diffusion-advection competition system with heterogeneity vs homogeneity ⋮ Asymptotic behaviour of a reaction–diffusion model with a quiescent stage ⋮ Dynamics for a nonlocal competition system with a free boundary ⋮ Resonance Phenomena in a Singular Perturbation Problem in the Case of Exchange of Stabilities ⋮ On diffusive stability of Eigen's quasispecies model ⋮ Directed vs regular diffusion strategy: evolutionary stability analysis of a competition model and an ideal free pair ⋮ Advection-dispersion across interfaces ⋮ A spatial SIS model with Holling II incidence rate ⋮ Asymptotic Profiles of Solutions and Propagating Terrace for a Free Boundary Problem of Nonlinear Diffusion Equation with Positive Bistable Nonlinearity ⋮ Global dynamics of a Lotka–Volterra competitive system from river ecology: general boundary conditions ⋮ Analysis of Propagation for Impulsive Reaction-Diffusion Models ⋮ Spatial Invasion of a Birth Pulse Population with Nonlocal Dispersal ⋮ Persistence and Extinction of Population in Reaction-Diffusion-Advection Model with Weak Allee Effect Growth ⋮ Bifurcation Analysis of a Diffusive Predator–Prey Model with Bazykin Functional Response ⋮ On the identification of a nonlinear term in a reaction–diffusion equation ⋮ Concentration phenomena in an integro-PDE model for evolution of conditional dispersal ⋮ NEW EXACT SOLUTIONS OF SPATIALLY AND TEMPORALLY VARYING REACTION-DIFFUSION EQUATIONS ⋮ Traveling wave solutions of Lotka–Volterra type two predators‐one prey model ⋮ Patterns Versus Spatial Heterogeneity—From a Variational Viewpoint ⋮ OPTIMAL RESOURCE ALLOCATION FOR A DIFFUSIVE POPULATION MODEL ⋮ Blowup and global existence of a free boundary problem with weak spatial source ⋮ SPATIAL PATTERN FORMATIONS IN DIFFUSIVE PREDATOR-PREY SYSTEMS WITH NON-HOMOGENEOUS DIRICHLET BOUNDARY CONDITIONS ⋮ Dynamics of a diffusive vaccination model with therapeutic impact and non-linear incidence in epidemiology ⋮ GLOBAL BIFURCATION FROM INTERVALS IN NONLINEAR STURM-LIOUVILLE PROBLEM WITH INDEFINITE WEIGHT FUNCTION ⋮ Fully Adaptive Newton--Galerkin Methods for Semilinear Elliptic Partial Differential Equations ⋮ The Effect of Diffusion on the Dynamics of a Predator-Prey Chemostat Model ⋮ Dynamics of a multi-strain malaria model with diffusion in a periodic environment