Stability, Steady‐State Bifurcations, and Turing Patterns in a Predator–Prey Model with Herd Behavior and Prey‐taxis

DOI10.1111/sapm.12165zbMath1373.35324OpenAlexW2593478941WikidataQ115526905 ScholiaQ115526905MaRDI QIDQ4588946

Xiaosong Tang, Yongli Song

Publication date: 6 November 2017

Published in: Studies in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1111/sapm.12165

Mathematics Subject Classification ID

PDEs in connection with biology, chemistry and other natural sciences (35Q92) Population dynamics (general) (92D25) Bifurcations in context of PDEs (35B32)

Related Items (69)

Pattern dynamics in a diffusive predator-prey model with hunting cooperations ⋮ Dynamics of the non-autonomous boy-after-girl system ⋮ Dynamics of a non-autonomous predator-prey system with Hassell-Varley-Holling II function response and mutual interference ⋮ Hopf bifurcation in a diffusive predator-prey model with a square-root singularity ⋮ Global bifurcation for a reaction-diffusion predator-prey model with Holling-II functional response and prey-taxis ⋮ Stationary pattern and bifurcation of a Leslie-Gower predator-prey model with prey-taxis ⋮ Pattern formation in a reaction-diffusion parasite-host model ⋮ Bifurcation structure of nonconstant positive steady states for a diffusive predator-prey model ⋮ Bifurcation analysis of a spatial vegetation model ⋮ Stability and double-Hopf bifurcations of a Gause-Kolmogorov-type predator-prey system with indirect prey-taxis ⋮ Pattern formation in the Holling-Tanner predator-prey model with predator-taxis. A nonstandard finite difference approach ⋮ Different Mechanisms of Pattern Formation in a Plankton Model with Cross-Diffusion and Fitness ⋮ Bifurcations and Traveling Wave Solutions of Lakshmanan–Porsezian–Daniel Equation with Parabolic Law Nonlinearity ⋮ Traveling wave solutions of the complex Ginzburg-Landau equation with Kerr law nonlinearity ⋮ Dynamic analysis of multi-factor influence on a Holling type II predator-prey model ⋮ Bifurcation dynamics of a reaction–diffusion predator–prey model with fear effect in a predator‐poisoned environment ⋮ Spatiotemporal dynamics in a diffusive predator-prey model with multiple Allee effect and herd behavior ⋮ Hopf and Turing-Hopf bifurcation analysis of a delayed predator-prey model with schooling behavior ⋮ Asymptotic analysis of impulsive dispersal predator-prey systems with Markov switching on finite-state space ⋮ Impacts of prey-taxis and nonconstant mortality on a spatiotemporal predator-prey system ⋮ Global dynamics of a stochastic reaction–diffusion predator–prey system with space-time white noise ⋮ Stationary and oscillatory patterns of a food chain model with diffusion and predator‐taxis ⋮ Bifurcation analysis of a diffusive predator–prey model with prey social behavior and predator harvesting ⋮ Bifurcations and exact traveling wave solutions of Gerdjikov-Ivanov equation with perturbation terms ⋮ Stationary pattern and Hopf bifurcation of a diffusive predator–prey model ⋮ Bifurcation analysis of a diffusive predator–prey model with hyperbolic mortality and prey-taxis ⋮ Hopf bifurcation analysis of a predator-prey model with prey refuge and fear effect under non-diffusion and diffusion ⋮ Spatiotemporal Dynamics of the Diffusive Mussel-Algae Model Near Turing-Hopf Bifurcation ⋮ Dynamic analysis of a diffusive predator-prey model with hunting cooperation functional response and prey-taxis ⋮ Nonlocal competition and spatial multi-peak periodic pattern formation in diffusive Holling-Tanner predator-prey model ⋮ Bifurcation branch of stationary solutions in a general predator-prey system with prey-taxis ⋮ Stability and bifurcation analysis of micro-electromechanical nonlinear coupling system with delay ⋮ Stability and Turing Patterns in a Predator–Prey Model with Hunting Cooperation and Allee Effect in Prey Population ⋮ DELAY INDUCED SUBCRITICAL HOPF BIFURCATION IN A DIFFUSIVE PREDATOR-PREY MODEL WITH HERD BEHAVIOR AND HYPERBOLIC MORTALITY ⋮ Spatiotemporal dynamics in a diffusive bacterial and viral diseases propagation model with chemotaxis ⋮ Impact of prey herd shape on the predator-prey interaction ⋮ Unnamed Item ⋮ Pattern formation of a predator-prey model with the cost of anti-predator behaviors ⋮ Unnamed Item ⋮ Spatiotemporal dynamics of a predator-prey system with prey-taxis and intraguild predation ⋮ Analysis of effects of delays and diffusion on a predator-prey system ⋮ Travelling wave solutions of the general regularized long wave equation ⋮ Spatiotemporal pattern formation and selection induced by nonlinear cross-diffusion in a toxic-phytoplankton-zooplankton model with Allee effect ⋮ Global bifurcation for a Holling-Tanner predator-prey model with prey-taxis ⋮ Chemotaxis induced complex dynamics in a novel viral infection model ⋮ Stability and Bifurcation Analysis of a Commensal Model with Additive Allee Effect and Nonlinear Growth Rate ⋮ Dynamics analysis of a predator-prey model with herd behavior and nonlocal prey competition ⋮ Spatio-temporal dynamics near the steady state of a planktonic system ⋮ Cross-diffusion induced Turing instability for a competition model with saturation effect ⋮ Periodic solution of a stage-structured predator-prey model incorporating prey refuge ⋮ Dynamics of a diffusive predator–prey model with herd behavior ⋮ Spatiotemporal complexity of a diffusive planktonic system with prey-taxis and toxic effects ⋮ Spatiotemporal patterns induced by Hopf bifurcations in a homogeneous diffusive predator-prey system ⋮ Dynamics in a delayed diffusive cell cycle model ⋮ A unified analysis of exact traveling wave solutions for the fractional-order and integer-order Biswas-Milovic equation: via bifurcation theory of dynamical system ⋮ Stability and bifurcation analysis of an amensalism model with weak allee effect ⋮ Spatiotemporal patterns induced by cross-diffusion in predator–prey model with prey herd shape effect ⋮ Traveling wave solutions of a generalized Burgers-\(\alpha\beta\) equation ⋮ Pattern Dynamics in a Predator–Prey Model with Schooling Behavior and Cross-Diffusion ⋮ Travelling wave solutions of Wu-Zhang system via dynamic analysis ⋮ Stability and spatiotemporal dynamics in a diffusive predator-prey model with nonlocal prey competition ⋮ Mathematical analysis of a diffusive predator-prey model with herd behavior and prey escaping ⋮ Pattern formation in a ratio-dependent predator-prey model with cross-diffusion ⋮ An algorithm for solving linear nonhomogeneous quaternion-valued differential equations and some open problems ⋮ Chemotaxis induced Turing bifurcation in a partly diffusive bacterial and viral diseases propagation model ⋮ EFFECT OF HERD SHAPE IN A DIFFUSIVE PREDATOR-PREY MODEL WITH TIME DELAY ⋮ HOPF BIFURCATION IN A DIFFUSIVE PREDATOR-PREY MODEL WITH HERD BEHAVIOR AND PREY HARVESTING ⋮ A non-autonomous Leslie-Gower model with Holling type IV functional response and harvesting complexity ⋮ Global solution and spatial patterns for a ratio-dependent predator-prey model with predator-taxis

This page was built for publication: Stability, Steady‐State Bifurcations, and Turing Patterns in a Predator–Prey Model with Herd Behavior and Prey‐taxis