论文标题
使用不变的歧管和全局分叉的反应扩散系统中多波解决方案的案例研究
A case study of multiple wave solutions in a reaction-diffusion system using invariant manifolds and global bifurcations
论文作者
论文摘要
进行了彻底的分析，以在受捕食者捕集模型启发的定性反应扩散系统中找到行进波。我们提供了来自标准的局部稳定性分析，数值分叉分析的严格结果，以及对表现出同质和杂斜连接的不变歧管的相关计算，以及与四个组件的相关行动波系统中的周期性轨道。这样一来，我们介绍并描述了一个不同行驶波解决方案的动物园。此外，同时性混乱是通过鞍焦和聚焦分叉以及Belyakov点表现出来的。还提出了焦点同型分叉附近的全局不变歧管的实际计算，以揭示模型中波动解决方案的多样性。
A thorough analysis is performed to find traveling waves in a qualitative reaction-diffusion system inspired by a predator-prey model. We provide rigorous results coming from a standard local stability analysis, numerical bifurcation analysis, and relevant computations of invariant manifolds to exhibit homoclinic and heteroclinic connections, and periodic orbits in the associated traveling wave system with four components. In so doing, we present and describe a zoo of different traveling wave solutions. In addition, homoclinic chaos is manifested via both saddle-focus and focus-focus bifurcations as well as a Belyakov point. An actual computation of global invariant manifolds near a focus-focus homoclinic bifurcation is also presented to unravel a multiplicity of wave solutions in the model.
