Effect of a protection zone in the diffusive Leslie predator-prey model

DOI10.1016/j.jde.2008.11.007zbMath1168.35444OpenAlexW1966280076MaRDI QIDQ1018391

Mingxin Wang, Rui Peng, Yihong Du

Publication date: 19 May 2009

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2008.11.007

zbMATH Keywords

positive solutionprey-predator modelboundary blow-up problemprotection zone

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Population dynamics (general) (92D25) Nonlinear elliptic equations (35J60) Variational methods for second-order elliptic equations (35J20)

Related Items

Dynamics and asymptotic profiles of endemic equilibrium for two frequency-dependent SIS epidemic models with cross-diffusion, Dynamics of Holling-type II prey–predator system with a protection zone for prey, Unnamed Item, Dynamics and pattern formation in a modified Leslie–Gower model with Allee effect and Bazykin functional response, A reaction-diffusion epidemic model with virus mutation and media coverage: theoretical analysis and numerical simulation, A diffusion-advection predator-prey model with a protection zone, A reaction–diffusion SIS epidemic model with saturated incidence rate and logistic source, On a rumor propagation model with spatial heterogeneity, Long-time behavior of a reaction-diffusion model with strong Allee effect and free boundary: effect of protection zone, Enhancing population persistence by a protection zone in a reaction-diffusion model with strong Allee effect, Effects of B-D functional response and protection zone on a predator-prey model, A diffusive SIS epidemic model with saturated incidence function in a heterogeneous environment ^*, Analysis of global stability and asymptotic properties of a cholera model with multiple transmission routes, spatial diffusion and incomplete immunity, Time delays and economic profit in fractional differential‐algebraic predator–prey model, Strong resonance bifurcations and state feedback control in a discrete prey-predator model with harvesting effect, Bifurcation analysis and simulations of a modified Leslie–Gower predator–prey model with constant‐type prey harvesting, Pattern Formation Scenario through Turing Instability in Interacting Reaction Diffusion Systems with Both Refuge and Nonlinear Harvesting, SPATIOTEMPORAL DYNAMICS OF A DIFFUSIVE LESLIE-TYPE PREDATOR–PREY MODEL WITH BEDDINGTON–DEANGELIS FUNCTIONAL RESPONSE, Spatiotemporal Dynamics of a Diffusive Leslie–Gower Predator–Prey Model with Ratio-Dependent Functional Response, Survival analysis of a single-species population model with fluctuations and migrations between patches, Analysis on a diffusive SI epidemic model with logistic source and saturation infection mechanism, Combined effects of the spatial heterogeneity and the functional response, Dynamics and patterns of a diffusive Leslie-Gower prey-predator model with strong Allee effect in prey, Bifurcations in a modified Leslie-Gower predator-prey discrete model with Michaelis-Menten prey harvesting, Qualitative analysis on a reaction-diffusion host-pathogen model with incubation period and nonlinear incidence rate, Spatial degeneracy vs functional response, Spatiotemporal Patterns of a Predator–Prey System with an Allee Effect and Holling Type III Functional Response, Dynamic analysis and optimal control of a fractional order singular Leslie-Gower prey-predator model, Varying total population enhances disease persistence: qualitative analysis on a diffusive SIS epidemic model, A diffusive predator-prey system with prey refuge and predator cannibalism, Asymptotic behavior of positive solutions to a predator-prey elliptic system with strong hunting cooperation in predators, Threshold dynamics of a reaction-diffusion-advection Leslie-Gower predator-prey system, The effect of protection zone on asymptotic dynamics of a reaction-diffusion model with a free boundary or unbounded boundary, Effect of cross-diffusion on the stationary problem of a Leslie prey-predator model with a protection zone, Dynamics of a diffusive prey-predator system with strong Allee effect growth rate and a protection zone for the prey, Qualitative analysis on an SIRS reaction-diffusion epidemic model with saturation infection mechanism, On a Diffusive Susceptible-Infected-Susceptible Epidemic Model with Mass Action Mechanism and Birth-Death Effect: Analysis, Simulations, and Comparison with Other Mechanisms, Dynamics of diffusive nutrient-microorganism model with spatially heterogeneous environment, Turing patterns of a strongly coupled predator-prey system with diffusion effects, Existence and attractivity of a periodic solution for a ratio-dependent Leslie system with feedback controls, Qualitative analysis of a diffusive SEIR epidemic model with linear external source and asymptomatic infection in heterogeneous environment, Analysis on a diffusive SIS epidemic model with logistic source, The protection zone of biological population, Analysis on a diffusive SIS epidemic model with saturated incidence rate and linear source in a heterogeneous environment, Uniqueness and stability of positive solutions for a diffusive predator-prey model in heterogeneous environment, Spatiotemporal patterns of a homogeneous diffusive predator-prey system with Holling type III functional response, Periodicity and attractivity of a ratio-dependent Leslie system with impulses, Bifurcations and asymptotic behavior of positive steady-states of an enzyme-catalyzed reaction–diffusion system, Coexistence states of a predator-prey model with cross-diffusion, An SIS epidemic reaction-diffusion model with spontaneous infection in a spatially heterogeneous environment, Unnamed Item, Necessary and sufficient conditions for existence of blow‐up solutions for elliptic problems in Orlicz–Sobolev spaces, Effect of cross-diffusion on the stationary problem of a prey-predator model with a protection zone, Fish-hook shaped global bifurcation branch of a spatially heterogeneous cooperative system with cross-diffusion, Stationary patterns of a prey-predator system with a protection zone and cross-diffusion of fractional type, Unnamed Item, Analysis on a diffusive SIRS epidemic model with logistic source and saturated incidence rate, Dynamics analysis on a chronic epidemic model with diffusion, Effect of cross-diffusion in the diffusion prey-predator model with a protection zone. II, Qualitative analysis on a diffusive SIS epidemic system with logistic source and spontaneous infection in a heterogeneous environment, Positive steady states of the S-K-T competition model with spatially heterogeneous interactions, Spatiotemporal dynamics analysis and optimal control method for an SI reaction-diffusion propagation model, The stability of bifurcating steady states for a spatially heterogeneous cooperative system with cross-diffusion, Dynamics of a diffusive Leslie-Gower predator-prey model in spatially heterogeneous environment, Asymptotic profile of the positive steady state for an SIS epidemic reaction-diffusion model: effects of epidemic risk and population movement, Uniqueness and non-uniqueness of steady states for a diffusive predator-prey-mutualist model with a protection zone, A robustness analysis of biological population models with protection zone, Stationary and non-stationary patterns of the density-suppressed motility model, Positive steady state solutions of a diffusive Leslie-Gower predator-prey model with Holling type II functional response and cross-diffusion, Protection Zones for Survival of Species in Random Environment, Qualitative analysis of steady states to the Sel'kov model, The role of protection zone on species spreading governed by a reaction-diffusion model with strong Allee effect, On travelling wave solutions of the diffusive Leslie-Gower model, Pattern formation of a biomass-water reaction-diffusion model, On the stability and Hopf bifurcation of a prey-generalist predator system with independent age-selective harvesting, Effect of the protection zone on coexistence of the species for a ratio-dependent predator-prey model, Persistence and almost periodic solutions for a discrete ratio-dependent Leslie system with feedback control, Positive solutions for Lotka-Volterra competition system with large cross-diffusion in a spatially heterogeneous environment, Uniqueness and global stability of positive stationary solution for a predator-prey system, Effect of harvesting quota and protection zone in a reaction-diffusion model arising from fishery management, Effect of cross-diffusion in the diffusion prey-predator model with a protection zone, Theoretical analysis on a diffusive SIR epidemic model with nonlinear incidence in a heterogeneous environment, The protection zone for biological population in random environment, Bifurcation analysis of modified Leslie-Gower predator-prey model with Michaelis-Menten type prey harvesting, Complexity and chaos control in a discrete-time prey-predator model, Positive solutions of a class of reaction-diffusion equations in spatially heterogeneous environment, Diffusive Holling type-II predator-prey system with harvesting of prey, Protection zone in a diffusive predator-prey model with Beddington-DeAngelis functional response, Qualitative analysis on a diffusive SIRS epidemic model with standard incidence infection mechanism, Bifurcation analysis and dynamic behavior to a predator-prey model with Beddington-DeAngelis functional response and protection zone, Qualitative analysis on an SIS epidemic reaction-diffusion model with mass action infection mechanism and spontaneous infection in a heterogeneous environment, Long-time behavior of a diffusive prey-predator system with Beddington-DeAngelis functional response in heterogeneous environment, A prey-predator model with harvesting for fishery resource with reserve area, Protection zone in a diffusive predator-prey model with Ivlev-type functional response, Effect of diffusion in a spatial SIS epidemic model with spontaneous infection, Analysis of a diffusive host-pathogen model with standard incidence and distinct dispersal rates, Qualitative analysis of a diffusive SIR epidemic model with saturated incidence rate in a heterogeneous environment, On a diffusive predator-prey model with nonlinear harvesting, Stability and dynamics of a fractional order Leslie-Gower prey-predator model, Steady-State Problem of an S-K-T Competition Model with Spatially Degenerate Coefficients, Analysis on a diffusive SIS epidemic system with linear source and frequency-dependent incidence function in a heterogeneous environment, Uniqueness and multiplicity of positive solutions for a diffusive predator–prey model in the heterogeneous environment, Dynamics of a modified Leslie-Gower model with double Allee effects, Analysis on a diffusive two-stage epidemic model with logistic growth and saturated incidence rates, Analysis on a diffusive SEI epidemic model with/without immigration of infected hosts, Existence and asymptotic profiles of the steady state for a diffusive epidemic model with saturated incidence and spontaneous infection mechanism, Effects of protection zone and nonlinear growth on a predator-prey model, Effects of dispersal for a predator-prey model in a heterogeneous environment, Nonlinear instability for a Leslie-Gower predator-prey model with cross diffusion, Asymptotic profiles of a diffusive SIRS epidemic model with standard incidence mechanism and a logistic source, The role of strong Allee effect and protection zone on a diffusive prey-predator model, Qualitative analysis on a diffusive prey-predator model with ratio-dependent functional response, On dynamics and stationary pattern formations of a diffusive predator-prey system with hunting cooperation, The effects of diffusion on the dynamics of a Lotka-Volterra predator-prey model with a protection zone, Global stability of spatially nonhomogeneous steady state solution in a diffusive Holling-Tanner predator-prey model, Positive solutions of a predator-prey model with cross-diffusion, Asymptotic profiles of a diffusive SIS epidemic model with vector-mediated infection and logistic source, Asymptotic dynamics of a logistic SIS epidemic reaction-diffusion model with nonlinear incidence rate, Protection zone in a modified Lotka-Volterra model

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the long-time limit of positive solutions to the degenerate logistic equation
• A diffusive predator-prey model with a protection zone
• Loops and branches of coexistence states in a Lotka--Volterra competition model
• The degenerate logistic model and a singularly mixed boundary blow-up problem
• Diffusion vs cross-diffusion: An elliptic approach
• Realization of prescribed patterns in the competition model.
• On the structure of the permanence region for competing species models with general diffusivities and transport effects
• Effects of a degeneracy in the competition model. I: Classical and generalized steady-state solutions
• Effects of a degeneracy in the competition model. II: Perturbation and dynamical behaviour
• Convergence in competition models with small diffusion coefficients
• Positive solutions with prescribed patterns in some simple semilinear equations
• Spatial heterogeneity of resources versus Lotka-Volterra dynamics
• A diffusive predator-prey model in heterogeneous environment
• Spatial patterns for population models in a heterogeneous environment
• Elliptic eigenvalue problems and unbounded continua of positive solutions of a semilinear elliptic equations
• A diffusive competition model with a protection zone
• On the effects of migration and spatial heterogeneity on single and multiple species
• Some global results for nonlinear eigenvalue problems
• Bifurcation from simple eigenvalues
• LOGISTIC TYPE EQUATIONS ON ℝ^N BY A SQUEEZING METHOD INVOLVING BOUNDARY BLOW-UP SOLUTIONS
• The properties of a stochastic model for the predator-prey type of interaction between two species
• Asymptotic behaviour of positive steady states to a predator—prey model
• Allee effect and bistability in a spatially heterogeneous predator-prey model
• Global Bifurcation of Positive Solutions in Some Systems of Elliptic Equations
• A priori bounds for positive solutions of nonlinear elliptic equations
• Competing Species near a Degenerate Limit
• Spatial Ecology via Reaction‐Diffusion Equations
• Positive steady states of the Holling–Tanner prey–predator model with diffusion
• Blow-Up Solutions for a Class of Semilinear Elliptic and Parabolic Equations
• Effects of Certain Degeneracies in the Predator-Prey Model
• Global Stability for a Class of Predator-Prey Systems
• SOME FURTHER NOTES ON THE USE OF MATRICES IN POPULATION MATHEMATICS