Turing–Hopf bifurcation analysis of a predator–prey model with herd behavior and cross-diffusion

In this paper, we consider a predator–prey model with herd behavior and cross-diffusion subject to homogeneous Neumann boundary condition. Firstly, the existence and priori bound of a solution for the model without cross-diffusion are shown. Then, by computing and analyzing the normal form on the ce...

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Bibliographic Details
Published inNonlinear dynamics Vol. 86; no. 1; pp. 73 - 89
Main Authors Tang, Xiaosong, Song, Yongli, Zhang, Tonghua
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.10.2016
Springer Nature B.V
Subjects
Automotive Engineering
Bifurcations
Boundary conditions
Canonical forms
Classical Mechanics
Computation
Computer simulation
Control
Diffusion
Dynamic tests
Dynamical Systems
Dynamics
Engineering
Hopf bifurcation
Manifolds
Mathematical models
Mechanical Engineering
Original Paper
Predator-prey simulation
Vibration
Cross-diffusion
Turing–Hopf bifurcation
Predator–prey model
Spatially inhomogeneous periodic solution
Herd behavior
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Summary:In this paper, we consider a predator–prey model with herd behavior and cross-diffusion subject to homogeneous Neumann boundary condition. Firstly, the existence and priori bound of a solution for the model without cross-diffusion are shown. Then, by computing and analyzing the normal form on the center manifold associated with the Turing–Hopf bifurcation, we find a wealth of spatiotemporal dynamics near the Turing–Hopf bifurcation point under suitable conditions. Furthermore, some numerical simulations to illustrate the theoretical analysis are carried out.
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ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-016-2873-3