一类具有不连续捕获的Lasota-Wazewska模型周期解存在性及稳定性分析

数学物理学报 ›› 2019, Vol. 39 ›› Issue (4): 785-796.

一类具有不连续捕获的Lasota-Wazewska模型周期解存在性及稳定性分析

阳超¹(),李润洁^2,*

¹ 长沙学院计算机工程与应用数学学院长沙 410022
² 湖南省火炬创业中心长沙 410013

收稿日期:2017-09-15 出版日期:2019-08-26 发布日期:2019-09-11
通讯作者: 李润洁 E-mail:yang0915@hnu.edu.cn
作者简介:阳超, E-mail:yang0915@hnu.edu.cn
基金资助:
国家自然科学基金(11801042);长沙市科技计划(K1705081)

Existence and Stability of Periodic Solution for a Lasota-Wazewska Model with Discontinuous Harvesting

Chao Yang¹(),Runjie Li^2,*

¹ Department of Mathematics and Computer Science, Changsha University, Changsha 410022
² Torch Entrepreneurship Center in Hunan Province, Changsha 410013

Received:2017-09-15 Online:2019-08-26 Published:2019-09-11
Contact: Runjie Li E-mail:yang0915@hnu.edu.cn
Supported by:
the NSFC(11801042);the Changsha Science and Technology Plan(K1705081)

摘要/Abstract

摘要：

该文研究了一类具有不连续捕获项的非光滑混合时滞Lasota-Wazewska模型.基于非光滑分析、Kakutani's不动点理论和常Lyapunov方法，建立了易于验证的与时滞无关的稳定性准则，同时保证模型的正周期解的存在性和全局指数稳定性，并给出了对应的仿真实例来验证该文中方法的正确性和有效性.

关键词: Lasota-Wazewska模型, 混合时滞, 不连续捕获, 正周期解, 指数稳定

Abstract:

In this paper, we study a class of mixed time-varying delayed Lasota-Wazewska model with discontinuous harvesting, which is described by a periodic nonsmooth dynamical system. Base on nonsmooth analysis, Kakutani's fixed point method and the generalized Lyapunov method, easily verifiable delay-independent criteria are established to ensure the existence and exponential stability of positive periodic solutions. Finally, we give an example to further illustrate the effectiveness of our main results.

Key words: Lasota-Wazewska model, Mixed delayed system, Discontinuous harvesting, Positive periodic solution, Exponential stability

中图分类号:

O193

阳超,李润洁. 一类具有不连续捕获的Lasota-Wazewska模型周期解存在性及稳定性分析[J]. 数学物理学报, 2019, 39(4): 785-796.

Chao Yang,Runjie Li. Existence and Stability of Periodic Solution for a Lasota-Wazewska Model with Discontinuous Harvesting[J]. Acta mathematica scientia,Series A, 2019, 39(4): 785-796.

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