论文标题
完整SKT模型中的Hopf分叉以及在哪里找到它们
Hopf bifurcations in the full SKT model and where to find them
论文作者
论文摘要
在本文中，我们考虑了Shigesada-Kawasaki-teramoto（SKT）模型，该模型介绍了描述竞争压力效应的交叉扩散术语。即使反应部分不存在激活剂抑制剂结构，交叉扩散也会破坏均匀平衡的稳定。但是，在完整的交叉扩散系统和弱竞争制度中，交叉扩散项具有相反的效果，并且该系统的分叉结构修改了增加种间竞争压力。在这里研究了分叉结构的主要变化，即均匀分支上的干草叉分叉的类型以及HOPF分叉点的存在。通过弱非线性分析，我们可以预测干草叉分叉的类型。增加了额外的交叉扩散系数，超临界的前两个干草叉分叉点成为次临界，导致多稳定区域的出现。种间竞争压力还会影响通过HOPF分叉点出现的稳定时间周期模式的可能出现。
In this paper, we consider the Shigesada-Kawasaki-Teramoto (SKT) model, which presents cross-diffusion terms describing competition pressure effects. Even though the reaction part does not present the activator-inhibitor structure, cross-diffusion can destabilise the homogeneous equilibrium. However, in the full cross-diffusion system and weak competition regime, the cross-diffusion terms have an opposite effect and the bifurcation structure of the system modifies increasing the interspecific competition pressure. The major changes in the bifurcation structure, the type of pitchfork bifurcations on the homogeneous branch, as well as the presence of Hopf bifurcation points are here investigated. Through weakly nonlinear analysis, we can predict the type of pitchfork bifurcation. Increasing the additional cross-diffusion coefficients, the first two pitchfork bifurcation points from super-critical become sub-critical, leading to the appearance of a multi-stability region. The interspecific competition pressure also influences the possible appearance of stable time-period spatial patterns appearing through a Hopf bifurcation point.
