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arXiv · 2002.09642

Double Hopf bifurcation in nonlocal reaction-diffusion systems with spatial average kernel

Zuolin Shen·Shanshan Chen·Junjie Wei
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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.

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Zuolin Shen, Shanshan Chen, Junjie Wei. 2020-02-22. Double Hopf bifurcation in nonlocal reaction-diffusion systems with spatial average kernel. https://arxiv.org/abs/2002.09642

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