恐惧效应对带时滞的反应扩散捕食系统的稳定区间的影响

摘要/Abstract

摘要：

该文结合理论推导和数值模拟两个方面研究了带有恐惧效应和时滞效应的反应扩散捕食-食饵模型的动力学.首先研究了系统的正平衡点的存在性和稳定性.其次，通过线性稳定性分析研究了系统的Hopf分支问题，结果表明恐惧效应影响Hopf分支点，继而影响着系统的稳定区间.最后，通过数值模拟验证了理论结果，并发现恐惧效应与稳定区间的非线性关系，即随着恐惧效应的持续增加，系统将会由稳定状态变为不稳定状态，再变为稳定状态.

关键词: 恐惧效应, Hopf分支, 时滞, 扩散, 捕食-食饵系统

Abstract:

This paper combines theoretical derivation and numerical simulation to study the dynamics of a delayed reaction-diffusion predator-prey model with fear effect. First, the existence and stability of the positive equilibrium point of the system are studied. Secondly, the Hopf bifurcation problem of the system is studied through linear stability analysis. The results show that the fear effect affects the Hopf bifurcation point, and then affects the stability interval of the system. Finally, the theoretical results are verified by numerical simulations, and the nonlinear relationship between the fear effect and the stability interval is found, that is, as the fear effect continues to increase, the system will change from a stable state to an unstable state, and then to a stable state.

Key words: Fear effect, Hopf bifurcation, Delay, Diffusion, Predator-prey system

中图分类号:

O175.2

孙悦,张道祥,周文. 恐惧效应对带时滞的反应扩散捕食系统的稳定区间的影响[J]. 数学物理学报, 2021, 41(6): 1980-1992.

Yue Sun,Daoxiang Zhang,Wen Zhou. The Influence of Fear Effect on Stability Interval of Reaction-Diffusion Predator-Prey System with Time Delay[J]. Acta mathematica scientia,Series A, 2021, 41(6): 1980-1992.

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参考文献 24

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恐惧交应$k_0$	Hopf分支临界值$\tau_0$	平衡点$E_(u_, v_*)$
2	6.0441	(1.5819, 0.6418)
3	1.9491	(1.2469, 0.5458)
6	1.2727	(0.9279, 0.3908)
8	1.2269	(0.8453, 0.3354)
9.7	1.2199	(0.7997, 0.3015)
10	1.2201	(0.7931, 0.2964)
10.3	1.2205	(0.7868, 0.2915)
11	1.2222	(0.7733, 0.2808)
13	1.2308	(0.7416, 0.2548)
20	1.2732	(0.6748, 0.1958)
30	1.3265	(0.6269, 0.1501)
40	1.3665	(0.5997, 0.1229)
60	1.4222	(0.5690, 0.0913)
80	1.4572	(0.5517, 0.0730)
100	1.4822	(0.5405, 0.0610)

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