论文标题
基于内存的扩散系统中的双HOPF分叉分析
Double Hopf bifurcation analysis in the memory-based diffusion system
论文作者
论文摘要
在本文中，我们得出了用于计算基于内存的扩散系统中出现的双HOPF分叉的正常形式的算法，该算法通过采用基于内存的扩散系数和存储器延迟作为扰动参数。使用所获得的理论结果，我们研究了具有II型功能响应的捕食者捕集系统中双Hopf分叉点附近的动力学分类。我们展示了不同种类的稳定在空间不均匀的周期性解决方案的存在，从一种到另一种到另一种以及两种具有不同空间曲线的定期解决方案的过渡，通过改变基于内存的基于内存的扩散系数和内存延迟。
In this paper, we derive the algorithm for calculating the normal form of the double Hopf bifurcation that appears in a memory-based diffusion system via taking memory-based diffusion coefficient and the memory delay as the perturbation parameters. Using the obtained theoretical results, we study the dynamical classification near the double Hopf bifurcation point in a predator-prey system with Holling type II functional response. We show the existence of different kinds of stable spatially inhomogeneous periodic solutions, the transition from one kind to the other as well as the coexistence of two types of periodic solutions with different spatial profiles by varying the memory-based diffusion coefficient and the memory delay.
