Periodic Solutions of a Cooperative System with State Feedback Control

HUANG Ming-zhan, LIU Shou-zong, SONG Xin-yu

doi:10.13371/j.cnki.chin.q.j.m.2016.03.006

Chinese Quarterly Journal of Mathematics >

2016 , Vol. 31 >Issue 3: 279 - 287

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2016.03.006

Periodic Solutions of a Cooperative System with State Feedback Control

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1. College of Mathematics and Information Science,Xinyang Normal University2. Research Institute of Forest Resource Information Techniques,Chinese Academy of Forestry

HUANG Ming-zhan(1982-), female, native of Nanyang, Henan, a lecturer of Xinyang Normal University, Ph.D., engages in biomathematics; LIU Shou-zong(1984-), male, native of Puyang, Henan, a lecturer of Xinyang Normal University, M.S.D., engages in biomathematics; SONG Xin-yu(1961-), male, native of Xinyang, Henan, a professor of Xinyang Normal University, Ph.D., engages in biomathematics.

Received date: 2016-02-10

Online published: 2020-11-05

Supported by

Supported by the National Natural Science Foundation of China(11671346,11501489,11371306,11301453)； Supported by the Department of Education of Henan Province(14B110034)； Supported by the Nanhu Scholars Program of XYNU,Foundation and Frontier Project of Henan(152300410019)； Supported by the Youth Teacher Foundation of XYNU(2016GGJJ-14)；

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Abstract

In this paper,we propose a semi-continuous dynamical system to study the cooperative system with feedback control.Based on geometrical analysis and the analogue of Poincaré criterion,the existence and stability of the positive order one periodic solutions are given.Numerical results are carried out to illustrate the feasibility of our main results.

Key words： cooperative system; feedback control; order one periodic solution; orbitally asymptotically stable

Cite this article

HUANG Ming-zhan, LIU Shou-zong, SONG Xin-yu . Periodic Solutions of a Cooperative System with State Feedback Control[J]. Chinese Quarterly Journal of Mathematics, 2016 , 31(3) : 279 -287 . DOI: 10.13371/j.cnki.chin.q.j.m.2016.03.006

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