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

• Published in: Nonlinear dynamics Vol. 86; no. 1; pp. 73 - 89
• Main Authors: Tang, Xiaosong, Song, Yongli, Zhang, Tonghua
• Format: Journal Article
• Language: English
• 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

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...