Turing-Hopf bifurcation in the reaction-diffusion system with delay and Application a diffusive predator-prey model
Turing-Hopf bifurcation in the reaction-diffusion system with delay and Application a diffusive predator-prey model
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延迟反应扩散系统中的图灵-霍普夫分岔及扩散捕食者-被捕食模型的应用
DOI：
10.11948/2156-907x.20190015
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发表时间：
2019
影响因子：
1.1
通讯作者：
Yuan Yuan
中科院分区：
文献类型：
--
作者：
Yongli Song;Heping Jiang;Yuan Yuan
扩散驱动的图灵不稳定性与延迟诱导的霍普夫分岔之间的相互作用往往会产生丰富的时空动力学。在本文中，我们首先推导出了含时滞反应 - 扩散系统中图灵 - 霍普夫分岔相关的正规形算法，该算法可用于研究参数平面中图灵 - 霍普夫分岔点附近的时空动力学分类。然后，我们考虑一个具有弱阿利效应和时滞的扩散捕食 - 被捕食模型。通过研究由扩散和时滞诱导的图灵 - 霍普夫分岔相应正规形的动力学，该分岔点附近的时空动力学可分为六类。特别地，发现了稳定的空间均匀/非均匀周期解和稳态、两种稳定的空间非均匀周期解的共存、两种稳定的空间非均匀稳态的共存以及从一种时空模式到另一种时空模式的转变。
The interactions of diffusion-driven Turing instability and delayinduced Hopf bifurcation always give rise to rich spatiotemporal dynamics. In this paper, we first derive the algorithm for the normal forms associated with the Turing-Hopf bifurcation in the reaction-diffusion system with delay, which can be used to investigate the spatiotemporal dynamical classification near the Turing-Hopf bifurcation point in the parameter plane. Then, we consider a diffusive predator-prey model with weak Allee effect and delay. Through investigating the dynamics of the corresponding normal form of Turing-Hopf bifurcation induced by diffusion and delay, the spatiotemporal dynamics near this bifurcation point can be divided into six categories. Especially, stable spatially homogeneous/inhomogeneous periodic solutions and steady states, coexistence of two stable spatially inhomogeneous periodic solutions, coexistence of two stable spaially inhomogeneous steady states and the transition from one kind of spatiotemporal patterns to another are found.