论文标题
在扩散系统中，由记忆和一般延迟共同引起的空间均匀HOPF分叉
The spatially homogeneous Hopf bifurcation induced jointly by memory and general delays in a diffusive system
论文作者
论文摘要
在本文中，通过将对反应项的一般延迟纳入基于内存的扩散系统中，我们提出了一个具有内存延迟和一般延迟（例如，消化，妊娠，狩猎，狩猎，迁移和成熟延迟等）的扩散系统。我们首先得出一种用于计算拟议系统中HOPF分叉的正常形式的算法。开发的用于计算HOPF分叉正常形式的算法可用于研究HOPF分叉的方向和稳定性。作为一个真实应用，我们考虑了具有比率依赖性的holling类型-3功能响应的扩散捕食者 - 捕集模型，其中包括内存和妊娠延迟。首先研究了没有妊娠延迟的HOPF分叉分析，然后研究了带有内存和妊娠延迟的HOPF分叉分析。通过使用开发的算法来计算HOPF分叉的正常形式，发现了由记忆和一般延迟共同引起的超临界和稳定的空间均质周期溶液。通过数值模拟证实了我们的分析结果，还发现了稳定的空间均匀周期溶液。
In this paper, by incorporating the general delay to the reaction term in the memory-based diffusive system, we propose a diffusive system with memory delay and general delay (e.g., digestion, gestation, hunting, migration and maturation delays, etc.). We first derive an algorithm for calculating the normal form of Hopf bifurcation in the proposed system. The developed algorithm for calculating the normal form of Hopf bifurcation can be used to investigate the direction and stability of Hopf bifurcation. As a real application, we consider a diffusive predator-prey model with ratio-dependent Holling type-3 functional response, which includes with memory and gestation delays. The Hopf bifurcation analysis without gestation delay is first studied, then the Hopf bifurcation analysis with memory and gestation delays is studied. By using the developed algorithm for calculating the normal form of Hopf bifurcation, the supercritical and stable spatially homogeneous periodic solutions induced jointly by memory and general delays are found. The stable spatially homogeneous periodic solutions are also found by the numerical simulations which confirms our analytic result.
