时标上带有反馈控制的非自治两种群竞争系统的概周期解

数学物理学报 ›› 2017, Vol. 37 ›› Issue (4): 730-750.

时标上带有反馈控制的非自治两种群竞争系统的概周期解

李周红¹, 张丰硕¹, 曹进德^2,3, Alsaedi Ahmed⁴, Alsaadi Fuad E⁵

1 玉溪师范学院数学系云南玉溪 653100;
2 东南大学数学学院南京 210096;
3 Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia;
4 Nonlinear Analysis and Applied Mathematics Research Group, Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia;
5 Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia

收稿日期:2016-09-27 修回日期:2017-02-24 出版日期:2017-08-26 发布日期:2017-08-26
作者简介:李周红,E-mail:zhouhli@yeah.net;曹进德,E-mail:jdcao@seu.edu.cn
基金资助:
国家自然科学基金（61272530，11072059）、江苏省自然科学基金（BK2012741）、云南省自然科学基金（2014FD049）和玉溪师范学院青年教师支持计划

Almost Periodic Solution for a Non-Autonomous Two Species Competitive System with Feedback Controls on Time Scales

Li Zhouhong¹, Zhang Fengshuo¹, Cao Jinde^2,3, Alsaedi Ahmed⁴, Alsaadi Fuad E⁵

1 Department of Mathematics, Yuxi Normal University, Yunnan Yuxi 653100, China;
2 School of Mathematics, Southeast University, Nanjing 210096, China;
3 Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia;
4 Nonlinear Analysis and Applied Mathematics Research Group, Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia;
5 Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Received:2016-09-27 Revised:2017-02-24 Online:2017-08-26 Published:2017-08-26
Supported by:
Supported by the NSFC (61272530,1072059), the Natural Science Foundation of Jiangsu Province (BK2012741), the Natural Science Foundation of Yunnan Province (2014FD049) and the Young Teacher Program of Yuxi Normal University

摘要/Abstract

摘要： 该文利用时标理论，研究了一类时标上带有反馈控制的非自治两种群竞争系统.首先应用微分不等式和比较原理得到了系统的持久性，在此基础上，构造了一个合适的Lyapunov泛函，得到系统存在概周期解的充分条件.进一步，应用一个例子的数值模拟验证了该文结果的有效性.

关键词: 概周期解, 持久, 竞争系统, 反馈控制, 时标

Abstract: In this paper, applying the time scales calculus theory, we first study the permanence for a non-autonomous two species competitive system with feedback controls on time scales. Based on the permanence result, by the comparison theorems of the differential equation and constructing a suitable Lyapunov functional, we establish sufficient conditions on the existence of almost periodic solution of the considered system. Moreover, an example along with its numerical simulation is employed to illustrate effectiveness of our main results.

Key words: Almost periodic solution, Permanence, Competitive model, Feedback controls, Time scales

中图分类号:

O175.13

李周红, 张丰硕, 曹进德, Alsaedi Ahmed, Alsaadi Fuad E. 时标上带有反馈控制的非自治两种群竞争系统的概周期解[J]. 数学物理学报, 2017, 37(4): 730-750.

Li Zhouhong, Zhang Fengshuo, Cao Jinde, Alsaedi Ahmed, Alsaadi Fuad E. Almost Periodic Solution for a Non-Autonomous Two Species Competitive System with Feedback Controls on Time Scales[J]. Acta mathematica scientia,Series A, 2017, 37(4): 730-750.

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