时间尺度上多时滞 GA- 捕食系统周期解的存在性和稳定性研究

中图分类号：O193 文献标志码：A

Abstract： This paper studies the existence and stability of periodic solutions for the Gilpin-Ayala（GA） predation system with multiple delays on time scales. By using Mawhin’s coincidence degree theory and inequality techniques， it bypasses the difficulty of direct solution and demonstrates the existence of solutions from a topological perspective， thereby giving the existence domain of solutions. After that， we consider the stability of this periodic solution and study it by variable substitution and using Lyapunov stability theory. Finally， an example is given to illustrate the validity of the conclusion.

Keywords： GA-predation ecosystem; time delay; time scale; the existence of periodic solutions; global asymptotic stability.

MR（2020） Subject Classiffcation： 34C25；34D20

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作者简介：冯梦娇。2001.10，女，四川成都，汉，硕士 研究方向：随机微分方程与无穷维动力系统