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

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• 作者：Xiaosong Tang ; Yongli Song ; Tonghua Zhang
• 关键词：Predator–prey model ; Herd behavior ; Cross ; diffusion ; Turing–Hopf bifurcation ; Spatially inhomogeneous periodic solution
• 刊名：Nonlinear Dynamics
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：86
• 期：1
• 页码：73-89
• 全文大小：2,665 KB
• 刊物类别：Engineering
• 刊物主题：Vibration, Dynamical Systems and Control
  Mechanics
  Mechanical Engineering
  Automotive and Aerospace Engineering and Traffic
  
• 出版者：Springer Netherlands
• ISSN：1573-269X
• 卷排序：86

文摘

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.