Spatiotemporal complexity in a Leslie-Gower type predator-prey model near Turing-Hopf point

被引：9
作者：
Chen, Mengxin [1 ]
Wu, Ranchao [2 ,3 ]
Liu, Hongxia [2 ,3 ]
Fu, Xiaoxue [2 ,3 ]
机构：
[1] Henan Normal Univ, Coll Math & Informat Sci, Xinxiang 453007, Henan, Peoples R China
[2] Anhui Univ, Sch Math, Hefei 230601, Peoples R China
[3] Anhui Univ, Ctr Pure Math, Hefei 230601, Peoples R China
来源：
CHAOS SOLITONS & FRACTALS | 2021年 / 153卷
基金：
中国国家自然科学基金;
关键词：
Predator-prey model; Turing-Hopf bifurcation; Weakly nonlinear analysis; Spatiotemporal pattern; SECONDARY INSTABILITIES; DIFFUSION; BIFURCATION; DYNAMICS; PATTERNS; STABILITY; SYSTEM;
D O I：
10.1016/j.chaos.2021.111509
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The Leslie-Gower type predator-prey system with the ratio-dependent Holling III functional response and Neumann boundary conditions is investigated in this paper. First, the boundedness results of both parabolic and elliptic equations are presented. Hereafter, the existence of the codimension-two TuringHopf point (C2THP) is identified, where the Turing and the Hopf modes intersect. To further explore the spatiotemporal dynamics near the C2THP, it is necessary to derive the amplitude equations, however, there are few results about that in the two-dimensional domain. Here the method of weakly nonlinear analysis is adopted to derive the amplitude equations. The temporal patterns, hexagonal patterns, and plane wave patterns, as well as the sufficient conditions of their existence and stability, can be presented through amplitude equations. (c) 2021 Elsevier Ltd. All rights reserved.
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页数：15
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