Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (1): 245-268.

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On a Nonlinear Non-Autonomous Ratio-Dependent Food Chain Model with Delays and Feedback Controls

Changyou Wang1(),Nan Li2,*(),Tao Jiang3,4,*(),Qiang Yang1   

  1. 1 College of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610225
    2 Department of Applied Mathematics, Southwestern University of Finance and Economics, Chengdu 610074
    3 Control Engineering College, Chengdu University of Information Technology, Chengdu 610225
    4 State key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110169
  • Received:2020-09-26 Online:2022-02-26 Published:2022-02-23
  • Contact: Nan Li,Tao Jiang E-mail:wangchangyou417@163.com;2972028881@qq.com;jiangtop@126.com
  • Supported by:
    the Robot Research Fund of State Key Laboratory(2019-O13);the Science Research Project of Sichuan Provincial Department(2021YFH0069);the Talent Introduction Project of Chengdu University of Information Engineering(KYTZ201820);the Sichuan Science and Technology Program(21ZYZYTS0158)

Abstract:

In this paper, we study a 3-species nonlinear non-autonomous ratio-dependent food chain system with delays and feedback controls. Firstly, based on the theory of delay differential inequality, some new analytical methods are developed and a suitable Lyapunov function is constructed. Secondly, sufficient conditions for the permanence and global attractivity of positive solutions for the system are obtained. Thirdly, by using the theoretical analysis and fixed point theory, the corresponding periodic systems are discussed, and the conditions for the existence, uniqueness and stability of positive periodic solutions of periodic systems are established. Moreover, we give some numerical simulations to prove that our theoretical analysis are correct. Finally, we still give an numerical example for the corresponding stochastic food chain model with multiplicative noise sources, and achieve new interesting change process of the solution for the model.

Key words: Delay, Ratio-Dependent, Feedback Control, Permanence, Global Attractive, Periodic solution

CLC Number: 

  • O175.12
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