Double Hopf bifurcation in nonlocal reaction-diffusion systems with spatial average kernel
Dynamical Systems
2020-02-25 v1
Abstract
In this paper, we consider a general reaction-diffusion system with nonlocal effects and Neumann boundary conditions, where a spatial average kernel is chosen to be the nonlocal kernel. By virtue of the center manifold reduction technique and normal form theory, we present a new algorithm for computing normal forms associated with the codimension-two double Hopf bifurcation of nonlocal reaction-diffusion equations. The theoretical results are applied to a predator-prey model, and complex dynamic behaviors such as spatially nonhomogeneous periodic oscillations and spatially nonhomogeneous quasi-periodic oscillations could occur.
Cite
@article{arxiv.2002.09642,
title = {Double Hopf bifurcation in nonlocal reaction-diffusion systems with spatial average kernel},
author = {Zuolin Shen and Shanshan Chen and Junjie Wei},
journal= {arXiv preprint arXiv:2002.09642},
year = {2020}
}