论文标题
与空间平均内核的非局部反应扩散系统中的双HOPF分叉
Double Hopf bifurcation in nonlocal reaction-diffusion systems with spatial average kernel
论文作者
论文摘要
在本文中，我们考虑了具有非局部效应和诺伊曼边界条件的一般反应扩散系统，其中选择空间平均内核作为非局部内核。借助中心流动技术和正常形式理论，我们提出了一种用于计算与非本地反应 - 扩散方程的双重HOPF分叉相关的正常形式的新算法。理论结果应用于捕食者捕集模型，可能会发生复杂的动态行为，例如空间非均匀的周期性振荡和空间非均匀的准周期性振荡。
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.
