年龄等级结构捕食系统的平衡态与稳定性  

Equilibria and Stability for a Predator-prey System of Hierarchical Age-structured Populations

作　　者：何泽荣[1] HE Zerong(Institute of Operational Research and Cybernetics,Hangzhou Dianzi University,Hangzhou,Zhejiang,310018,P.R.China)

机构地区：[1]杭州电子科技大学运筹与控制研究所,杭州浙江310018

出　　处：《数学进展》2021年第3期437-450,共14页Advances in Mathematics（China）

基　　金：国家自然科学基金(No.11871185);浙江省自然科学基金(No.LY18A010010)。

摘　　要：本文旨在探索基于个体等级差异的捕食种群系统的平衡态存在性及稳定性.借助非线性映射的非零不动点结果确立了系统正平衡态的存在性,运用压缩算子半群法获得了渐近稳定性判据,由扰动算子的特征值导出了不稳定条件.对于零解给出了全局稳定性判别法.This article concerns the existence and stability for equilibria of a predator-prey system of hierarchical age-structured populations.We show that there is at least one positive equilibrium via a result for non-zero fixed point of nonlinear mappings,obtain the criteria for asymptotical stability by means of a contraction semigroup of linear operators,and derive some conditions for the instability.Furthermore,we present the conditions which guarantee the global stability for zero state.

关 键 词：个体等级 捕食模型 平衡态 稳定性 算子半群 

分 类 号：O175.6[理学—数学]