Dynamics of two-species Holling type-II predator-prey system with cross-diffusion

被引：6

作者：

Ma, Li ^{[1
]}

Wang, Huatao ^{[2
]}

Gao, Jianping ^{[2
]}

机构：

[1] Guangdong Polytech Sci & Technol, Comp Engn Tech Coll, Artificial Intelligence Coll, Zhuhai 519090, Guangdong, Peoples R China

[2] Gannan Normal Univ, Coll Math & Comp, Ganzhou 341000, Jiangxi, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2023年 / 365卷

基金：

中国国家自然科学基金;

关键词：

Generalized solutions; Nonlinear cross diffusion; Leray-Schauder degree; Pattern formation; Lyapunov-Schmidt reduction; PATTERN-FORMATION; STEADY-STATES; CHEMOTAXIS SYSTEM; GLOBAL EXISTENCE; BIFURCATION; MODEL; UNIQUENESS; STABILITY;

D O I：

10.1016/j.jde.2023.04.035

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we are devoted to studying a Holling type-II predator-prey system with cross diffusion. First of all, by a series of estimates, we establish the global existence of generalized solutions under some proper assumptions. By analyzing the distribution of eigenvalues, we investigate the local and global stability of the constant solution and also consider the steady state bifurcation and Hopf bifurcation near the constant steady state in details. In addition, the nonexistence of non-constant steady states is also investigated when diffusion rate d is large enough. Finally, sufficient conditions ensuring the existence of non-constant steady states are obtained by using Leray-Schauder degree theory. (c) 2023 Elsevier Inc. All rights reserved.

引用

页码：591 / 635

页数：45

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