Spatiotemporal Complexity of Plankton and Fish Dynamics
From MaRDI portal
Publication:3151329
DOI10.1137/S0036144502404442zbMath1001.92050OpenAlexW1974301594MaRDI QIDQ3151329
Horst Malchow, Irene A. Tikhonova, Bai-Lian Li, Alexander B. Medvinsky, Sergei V. Petrovskii
Publication date: 15 October 2002
Published in: SIAM Review (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/s0036144502404442
Reaction-diffusion equations (35K57) Dynamical systems in biology (37N25) Ecology (92D40) Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics (82C41)
Related Items
Analysis of a nutrient-phytoplankton model in the presence of viral infection ⋮ Learning nonlinear turbulent dynamics from partial observations via analytically solvable conditional statistics ⋮ Patterns formations in a diffusive ratio-dependent predator-prey model of interacting populations ⋮ Soliton-like phenomena in one-dimensional cross-diffusion systems: a predator--prey pursuit and evasion example ⋮ Minimal model of plankton systems revisited with spatial diffusion and maturation delay ⋮ Spatiotemporal dynamics of reaction-diffusion models of interacting populations ⋮ Turing pattern formation in a predator-prey system with cross diffusion ⋮ Delay-driven spatial patterns in a predator-prey model with constant prey harvesting ⋮ Finite element approximation of a spatially structured metapopulation PDE model ⋮ Numerical analysis of a first-order in time implicit-symplectic scheme for predator-prey systems ⋮ A multigrid preconditioned numerical scheme for a reaction-diffusion system ⋮ Bifurcation analysis of a diffusive predator-prey model with ratio-dependent Holling type III functional response ⋮ Prey-predator model with a nonlocal bistable dynamics of prey ⋮ Positive steady states for a prey-predator model with some nonlinear diffusion terms ⋮ The dynamics of a diffusive nutrient-algae model based upon the Sanyang wetland ⋮ Spatiotemporal complexity of the nutrient-phytoplankton model ⋮ Allee-effect-induced instability in a reaction-diffusion predator-prey model ⋮ Positive symplectic integrators for predator-prey dynamics ⋮ Wave of chaos in a diffusive system: generating realistic patterns of patchiness in plankton-fish dynamics ⋮ Spatiotemporal complexity of a predator-prey system with constant harvest rate ⋮ Exploring dynamical complexity in diffusion driven predator-prey systems: effect of toxin producing phytoplankton and spatial heterogeneities ⋮ An analysis of a predator-prey model with both diffusion and migration ⋮ Emergent impacts of quadratic mortality on pattern formation in a predator-prey system ⋮ Pattern formation in a cross-diffusive ratio-dependent predator-prey model ⋮ Impacts of additional food on diffusion induced instabilities in a predator-prey system with mutually interfering predator ⋮ Dynamic behaviour of a reaction-diffusion predator-prey model with both refuge and harvesting ⋮ Potential Turing instability and application to plant-insect models ⋮ Cross-diffusion driven instability in a predator-prey system with cross-diffusion ⋮ Global bifurcation analysis and pattern formation in homogeneous diffusive predator-prey systems ⋮ Pattern formations of an epidemic model with Allee effect and time delay ⋮ Qualitative analysis of a diffusive prey-predator model ⋮ Turing instabilities and spatio-temporal chaos in ratio-dependent Holling-Tanner model ⋮ Regime shifts and ecological catastrophes in a model of plankton-oxygen dynamics under the climate change ⋮ Waves analysis and spatiotemporal pattern formation of an ecosystem model ⋮ The spatial patterns through diffusion-driven instability in a predator-prey model ⋮ Role of instant nutrient replenishment on plankton dynamics with diffusion in a closed system: A pattern formation ⋮ Pattern formation in a diffusive ratio-dependent Holling-Tanner predator-prey model with Smith growth ⋮ Pattern formation in a semi-ratio-dependent predator-prey system with diffusion ⋮ Global existence and boundedness in a reaction-diffusion-taxis system with three species ⋮ Pattern self-organization and pattern transition on the route to chaos in a spatiotemporal discrete predator-prey system ⋮ Predator-prey equations with constant harvesting and planting ⋮ Existence of complex patterns in the Beddington-DeAngelis predator-prey model ⋮ Pattern formation of a predator-prey model with the cost of anti-predator behaviors ⋮ Spatiotemporal dynamics of a predator-prey system with linear harvesting rate ⋮ Nonlinear analysis in a nutrient-algae-zooplankton system with sinking of algae ⋮ Stability and Hopf bifurcation analysis of a nutrient-phytoplankton model with delay effect ⋮ Spatial complexity of a predator-prey model with Holling-type response ⋮ Stability and dynamical analysis of a biological system ⋮ Spatiotemporal pattern formation and selection induced by nonlinear cross-diffusion in a toxic-phytoplankton-zooplankton model with Allee effect ⋮ Global asymptotic stability and equiasymptotic stability for a time-varying phytoplankton-zooplankton-fish system ⋮ Modeling and analysis of inhibitory effect in plankton-fish model: application to the hypertrophic Swarzedzkie Lake in Western Poland ⋮ Pattern dynamics of a spatial epidemic model with time delay ⋮ On travelling wave solutions of the diffusive Leslie-Gower model ⋮ Turing instability and pattern induced by cross-diffusion in a predator-prey system with Allee effect ⋮ Hopf bifurcation and spatial patterns of a delayed biological economic system with diffusion ⋮ Spatial dynamics of a nutrient-phytoplankton system with toxic effect on phytoplankton ⋮ Spatiotemporal dynamics and spatial pattern in a diffusive intraguild predation model with delay effect ⋮ Efficient numerical methods for spatially extended population and epidemic models with time delay ⋮ Transition from wave pattern to stationary pattern in a spatial predator-prey system with delay ⋮ Existence of spatial patterns in a predator-prey model with self- and cross-diffusion ⋮ Pattern formation and control of spatiotemporal chaos in a reaction diffusion prey-predator system supplying additional food ⋮ Patterned solutions of a homogenous diffusive predator-prey system of Holling type-III ⋮ Local dynamics of a diffusive predator-prey model in spatially heterogeneous environment ⋮ Traveling wave fronts of a single species model with cannibalism and nonlocal effect ⋮ Pattern formation of a predator-prey model ⋮ Complex patterns in a space- and time-discrete predator-prey model with Beddington-DeAngelis functional response ⋮ Hopf and steady state bifurcation analysis in a ratio-dependent predator-prey model ⋮ Interspecies competition between prey and two different predators with Holling IV functional response in diffusive system ⋮ Dynamics and pattern formation in a diffusive predator-prey system with strong Allee effect in prey ⋮ Solution of lambda-omega systems: Theta-schemes and multigrid methods ⋮ Self-organized wave pattern in a predator-prey model ⋮ Pattern formation in predator-prey model with delay and cross diffusion ⋮ Multiple bifurcations in a delayed predator-prey diffusion system with a functional response ⋮ Analysis of Bogdanov-Takens bifurcations in a spatiotemporal harvested-predator and prey system with Beddington-DeAngelis-type response function ⋮ Hopf bifurcation and harvesting control of a bioeconomic plankton model with delay and diffusion terms ⋮ Additional food induced Turing patterns for a diffusive predator-prey model ⋮ About reaction-diffusion systems involving the Holling-type II and the Beddington-DeAngelis functional responses for predator-prey models ⋮ A model for \textit{Vibrio cholerae} colonization of the human intestine ⋮ Spatial instabilities untie the exclusion-principle constraint on species coexistence ⋮ Ecological chaos and the choice of optimal harvesting policy ⋮ The complex dynamics of a stochastic toxic-phytoplankton-zooplankton model ⋮ Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator-prey system ⋮ Spatio-temporal Bazykin's model with space-time nonlocality ⋮ Global analysis and optimal harvesting for a hybrid stochastic phytoplankton-zooplankton-fish model with distributed delays ⋮ Dynamical complexities and pattern formation in an eco-epidemiological model with prey infection and harvesting ⋮ The stability and bifurcation of homogeneous diffusive predator-prey systems with spatio-temporal delays ⋮ Non-existence of non-constant positive steady states of two Holling type-II predator-prey systems: strong interaction case ⋮ Bifurcation in infinite dimensional spaces and applications in spatiotemporal biological and chemical models ⋮ Spatiotemporal pattern formation in a diffusive predator-prey system: An analytical approach ⋮ Stability of spatial patterns in a diffusive oxygen-plankton model with time lag effect ⋮ Efficient nonlinear optimal smoothing and sampling algorithms for complex turbulent nonlinear dynamical systems with partial observations ⋮ Three-dimensional pattern dynamics of a fractional predator-prey model with cross-diffusion and herd behavior ⋮ Cross-diffusion effects on stationary pattern formation in the Fitzhugh-Nagumo model ⋮ Spatiotemporal dynamics in a diffusive predator-prey system with Beddington-DeAngelis functional response ⋮ Stability and Hopf bifurcation of a diffusive plankton model with time-delay and mixed nonlinear functional responses ⋮ Spatiotemporal (target) patterns in sub-diffusive predator-prey system with the Caputo operator ⋮ Spatiotemporal pattern selection in a nontoxic-phytoplankton -- toxic-phytoplankton -- zooplankton model with toxin avoidance effects ⋮ Biological control via ``ecological damping: an approach that attenuates non-target effects ⋮ Estimates of size of cycle in a predator-prey system ⋮ Spatiotemporal patterns in an excitable plankton system with lysogenic viral infection ⋮ Analytical detection of stationary turing pattern in a predator-prey system with generalist predator ⋮ ROLE OF SPACE IN AN ECO-EPIDEMIC PREDATOR-PREY SYSTEM WITH THE EFFECT OF FEAR AND SELECTIVE PREDATION ⋮ Stability and errors estimates of a second-order IMSP scheme ⋮ Spatiotemporal dynamics of a predator-prey system with fear effect ⋮ Stationary and oscillatory patterns of a food chain model with diffusion and predator‐taxis ⋮ Numerical analysis of polio model: A mathematical approach to epidemiological model using derivative with Mittag–Leffler Kernel ⋮ Self-organization of nested patterns in a coupled spatiotemporal phytoplankton-zooplankton system ⋮ Double-Hopf bifurcation and pattern formation of a Gause-Kolmogorov-type system with indirect prey-taxis and direct predator-taxis ⋮ Effects of diffusion and advection on predator-prey dynamics in closed environments ⋮ Dynamics comparison between non-spatial and spatial systems of the plankton-fish interaction model ⋮ Stability switches and chaos induced by delay in a reaction-diffusion nutrient-plankton model ⋮ IMSP schemes for spatially explicit models of cyclic populations and metapopulation dynamics ⋮ Delay driven spatiotemporal chaos in single species population dynamics models ⋮ Stability analysis in a diffusional immunosuppressive infection model with delayed antiviral immune response ⋮ Bifurcation Analysis and Spatio-Temporal Patterns of a Prey–Predator Model with Hunting Cooperation ⋮ Allee effect and bistability in a spatially heterogeneous predator-prey model ⋮ Stability Switches and Chaos in a Diffusive Toxic Phytoplankton–Zooplankton Model with Delay ⋮ Global existence of solutions and uniform persistence of a diffusive predator-prey model with prey-taxis ⋮ Predator cannibalism can give rise to regular spatial pattern in a predator-prey system ⋮ OBSERVABILITY OF CHAOS AND CYCLES IN ECOLOGICAL SYSTEMS: LESSONS FROM PREDATOR–PREY MODELS ⋮ Detection and computation of high codimension bifurcations in diffuse predator-prey systems ⋮ Bifurcation Analysis and Spatiotemporal Patterns in a Diffusive Predator–Prey Model ⋮ Hunting cooperation among slowly diffusing specialist predators can induce stationary Turing patterns ⋮ Spatiotemporal pattern formation in a prey–predator model with generalist predator ⋮ Spatiotemporal dynamics of two generic predator–prey models ⋮ Spatially dependent parameter estimation and nonlinear data assimilation by autosynchronization of a system of partial differential equations ⋮ Bifurcation structure of nonconstant positive steady states for a diffusive predator-prey model ⋮ Bifurcation scenario of Turing patterns in prey-predator model with nonlocal consumption in the prey dynamics ⋮ Reaction-diffusion predator-prey-parasite system and spatiotemporal complexity ⋮ Cross diffusion induced spatiotemporal pattern in diffusive nutrient-plankton model with nutrient recycling ⋮ Stability and dynamic transition of a toxin-producing phytoplankton-zooplankton model with additional food ⋮ Bifurcation branch and stability of stationary solutions of a predator–prey model ⋮ A PREDATOR–PREY INTERACTION MODEL WITH SELF- AND CROSS-DIFFUSION IN AQUATIC SYSTEMS ⋮ Kinetic-fluid derivation and mathematical analysis of a nonlocal cross-diffusion-fluid system ⋮ Spatial dynamics of an epidemic model with nonlocal infection ⋮ Exploring the behavior of malware propagation on mobile wireless sensor networks: stability and control analysis ⋮ Turing patterns induced by cross-diffusion in a predator-prey system in presence of habitat complexity ⋮ Dynamic analysis of a heterogeneous diffusive prey-predator system in time-periodic environment ⋮ Complex Dynamics of Wetland Ecosystem with Nonlinear Harvesting: Application to Chilika Lake in Odisha, India ⋮ Invasion dynamics of a predator-prey system in closed advective environments ⋮ Different Mechanisms of Pattern Formation in a Plankton Model with Cross-Diffusion and Fitness ⋮ Spatiotemporal dynamics of Leslie-Gower predator-prey model with Allee effect on both populations ⋮ Computational analysis on Hopf bifurcation and stability for a consumer-resource model with nonlinear functional response ⋮ Dynamical behaviors of a predator-prey system with prey impulsive diffusion and dispersal delay between two patches ⋮ Modeling the invasion of recessive Bt-resistant insects: an impact on transgenic plants ⋮ DIFFUSIVE THREE SPECIES PLANKTON MODEL IN THE PRESENCE OF TOXIC PREY: APPLICATION TO SUNDARBAN MANGROVE WETLAND ⋮ The effect of slow spatial processes on emerging spatiotemporal patterns ⋮ Frequency modes of unstable spiral waves in two-dimensional Rosenzweig-MacArthur ecological networks ⋮ Diverse self-organized patterns and complex pattern transitions in a discrete ratio-dependent predator-prey system ⋮ Spatiotemporal complexity of patchy invasion in a predator-prey system with the Allee effect. ⋮ Finite-difference schemes for reaction-diffusion equations modeling predator-prey interactions in MATLAB ⋮ Global dynamics of a diffusive phytoplankton-zooplankton model with toxic substances effect and delay ⋮ The effects of obstacle size on periodic travelling waves in oscillatory reaction–diffusion equations ⋮ Prey-predator model with a nonlocal consumption of prey ⋮ Dynamics of a harvested predator-prey model with predator-taxis ⋮ Predator interference effects on biological control: the ``paradox of the generalist predator revisited ⋮ Invasion of pests resistant to Bt toxins can lead to inherent non-uniqueness in genetically modified Bt-plant dynamics: mathematical modeling ⋮ Parametric analysis of a predator-prey system stabilized by a top predator ⋮ Stabilizing Role of Nonlocal Interaction on Spatio-temporal Pattern Formation ⋮ Qualitative analysis on a reaction-diffusion nutrient-phytoplankton model with toxic effect of Holling-type II functional ⋮ Temporal Forcing Induced Pattern Transitions Near the Turing–Hopf Bifurcation in a Plankton System ⋮ Food web complexity analysis: effects of ecosystem changes ⋮ Instabilities in spatially extended predator-prey systems: spatio-temporal patterns in the neighborhood of Turing-Hopf bifurcations ⋮ Study of a Leslie-Gower predator-prey model with prey defense and mutual interference of predators ⋮ MODELING ZIKA TRANSMISSION DYNAMICS: PREVENTION AND CONTROL ⋮ Individual-based modeling of phytoplankton: evaluating approaches for applying the cell quota model ⋮ Approximated Spiral and Target Patterns in Bazykin’s Prey–Predator Model: Multiscale Perturbation Analysis ⋮ Pattern Formation and Synchronism in an Allelopathic Plankton Model with Delay in a Network ⋮ Spatial patterns through Turing instability in a reaction-diffusion predator-prey model ⋮ Stability analysis and finite volume element discretization for delay-driven spatio-temporal patterns in a predator-prey model ⋮ Turing Patterns in a Cross Diffusive System ⋮ Finite element approximation of spatially extended predator-prey interactions with the Holling type II functional response ⋮ 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 ⋮ A coupled plankton system with instantaneous and delayed predation ⋮ Propagation of Turing patterns in a plankton model ⋮ Numerical simulations of reaction–diffusion equations modeling prey–predator interaction with delay ⋮ An observer for an occluded reaction-diffusion system with spatially varying parameters ⋮ Oscillations and pattern formation in a slow-fast prey-predator system ⋮ DIFFUSION-DRIVEN INSTABILITIES AND SPATIO-TEMPORAL PATTERNS IN AN AQUATIC PREDATOR–PREY SYSTEM WITH BEDDINGTON–DEANGELIS TYPE FUNCTIONAL RESPONSE ⋮ EMERGENCE OF OSCILLATORY TURING PATTERNS INDUCED BY CROSS DIFFUSION IN A PREDATOR–PREY SYSTEM ⋮ Boundedness and global stability of a diffusive prey–predator model with prey-taxis ⋮ Turing instability and stationary patterns in a predator-prey systems with nonlinear cross-diffusions ⋮ Bifurcation analysis of a diffusive predator-prey system with nonmonotonic functional response ⋮ From Bistability to Coupling-Induced Oscillations in a Two-Habitat Model for the Rotifer Population Dynamics ⋮ Wave of Chaos and Pattern Formation in Spatial Predator-Prey Systems with Holling Type IV Predator Response ⋮ Pattern Formation of Competing Microorganisms in Sediments ⋮ SPATIOTEMPORAL TRANSMISSION DYNAMICS OF RECENT EBOLA OUTBREAK IN SIERRA LEONE, WEST AFRICA: IMPACT OF CONTROL MEASURES ⋮ Additive noise driven phase transitions in a predator-prey system ⋮ Emergence of Spatial Patterns in a Damaged Diffusive Eco-Epidemiological System ⋮ A three level finite element approximation of a pattern formation model in developmental biology ⋮ SPATIAL PATTERN IN A PREDATOR-PREY SYSTEM WITH BOTH SELF- AND CROSS-DIFFUSION ⋮ Mathematical modelling of plankton-oxygen dynamics under the climate change ⋮ MODELING INVASION OF PESTS RESISTANT TO Bt TOXINS PRODUCED BY GENETICALLY MODIFIED PLANTS: RECESSIVE VS. DOMINANT INVADERS ⋮ Spatiotemporal complexity in a predator-prey model with weak Allee effects ⋮ Spatiotemporal dynamics near the Turing-Hopf bifurcation in a toxic-phytoplankton-zooplankton model with cross-diffusion ⋮ IMSP schemes for spatially explicit models of cyclic populations and metapopulation dynamics ⋮ Invasive dynamics for a predator–prey system with Allee effect in both populations and a special emphasis on predator mortality ⋮ Unnamed Item ⋮ Deciphering Dynamics of Recent Epidemic Spread and Outbreak in West Africa: The Case of Ebola Virus ⋮ Spatiotemporal pattern in a self- and cross-diffusive predation model with the Allee effect ⋮ Chaos in the peroxidase–oxidase oscillator ⋮ EMERGENCE OF TRAVELING PATTERN IN A PREDATOR–PREY SYSTEM ⋮ Stability and Hopf bifurcation in a three-component planktonic model with spatial diffusion and time delay ⋮ AN EFFICIENT AND ACCURATE NUMERICAL SCHEME FOR TURING INSTABILITY ON A PREDATOR–PREY MODEL ⋮ Bifurcation analysis in a diffusive Segel-Jackson model ⋮ Self-organized spatial patterns due to diffusion in a Holling-Tanner predator-prey model ⋮ Turing instabilities in prey-predator systems with dormancy of predators ⋮ Instabilities and Patterns in Zooplankton-Phytoplankton Dynamics: Effect of Spatial Heterogeneity ⋮ Simple finite element methods for approximating predator-prey dynamics in two dimensions using \texttt{MATLAB} ⋮ Aggregation of toxin-producing phytoplankton acts as a defence mechanism – a model-based study ⋮ Pattern dynamics in a diffusive Rössler model
Uses Software
