DYNAMICS OF A STAGE-STRUCTURED POPULATION MODEL WITH A STATE-DEPENDENT DELAY

被引：5
作者：
Li, Shangzhi [1 ]
Guo, Shangjiang [1 ]
机构：
[1] China Univ Geosci, Sch Math & Phys, Wuhan 430074, Hubei, Peoples R China
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2020年 / 25卷 / 09期
关键词：
State-dependent delay; stage structure; positivity; equilibria; stability; OSCILLATING PERIODIC-SOLUTIONS; PREDATOR-PREY MODEL; GROWTH; STABILITY; BIFURCATION; EQUATION;
D O I：
10.3934/dcdsb.2020071
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper is devoted to the dynamics of a predator-prey model with stage structure for prey and state-dependent maturation delay. Firstly, positivity and boundedness of solutions are addressed to describe the population survival and the natural restriction of limited resources. Secondly, the existence, uniqueness, and local asymptotical stability of (boundary and coexisting) equilibria are investigated by means of degree theory and Routh-Hurwitz criteria. Thirdly, the explicit bounds for the eventual behaviors of the mature population are obtained. Finally, by means of comparison principle and two auxiliary systems, it observed that the local asymptotical stability of either of the positive interior equilibrium and the positive boundary equilibrium implies that it is also globally asymptotical stable if the derivative of the delay function around this equilibrium is small enough.
引用
收藏
页码：3523 / 3551
页数：29
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