数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (2): 429-448.doi: 10.1007/s10473-019-0209-3

• 论文 • 上一篇    下一篇

ON A MULTI-DELAY LOTKA-VOLTERRA PREDATOR-PREY MODEL WITH FEEDBACK CONTROLS AND PREY DIFFUSION

王长有1, 李楠2, 周钰谦1, 蒲兴成3, 李锐3   

  1. 1. College of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610225, China;
    2. Department of Applied Mathematics, Southwestern University of Finance and Economics, Chengdu 610074, China;
    3. College of Automation, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
  • 收稿日期:2018-02-22 修回日期:2018-06-28 出版日期:2019-04-25 发布日期:2019-05-06
  • 通讯作者: Nan LI E-mail:2972028881@qq.com
  • 作者简介:Changyou WANG,wangchangyou417@163.com;Yuqian ZHOU,cs97zyq@cuit.edu.cn;Xingcheng PU,puxc@cqupt.edu.cn;Rui LI,liruimath@qq.com
  • 基金资助:
    This work is supported by the Sichuan Science and Technology Program of China (2018JY0480), the Natural Science Foundation Project of CQ CSTC of China (cstc2015jcyjBX0135), the National Nature Science Fundation of China (61503053).

ON A MULTI-DELAY LOTKA-VOLTERRA PREDATOR-PREY MODEL WITH FEEDBACK CONTROLS AND PREY DIFFUSION

Changyou WANG1, Nan LI2, Yuqian ZHOU1, Xingcheng PU3, Rui LI3   

  1. 1. College of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610225, China;
    2. Department of Applied Mathematics, Southwestern University of Finance and Economics, Chengdu 610074, China;
    3. College of Automation, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
  • Received:2018-02-22 Revised:2018-06-28 Online:2019-04-25 Published:2019-05-06
  • Contact: Nan LI E-mail:2972028881@qq.com
  • Supported by:
    This work is supported by the Sichuan Science and Technology Program of China (2018JY0480), the Natural Science Foundation Project of CQ CSTC of China (cstc2015jcyjBX0135), the National Nature Science Fundation of China (61503053).

摘要: This article is focusing on a class of multi-delay predator-prey model with feedback controls and prey diffusion. By developing some new analysis methods and using the theory of differential inequalities as well as constructing a suitable Lyapunov function, we establish a set of easily verifiable sufficient conditions which guarantee the permanence of the system and the globally attractivity of positive solution for the predator-prey system. Furthermore, some conditions for the existence, uniqueness and stability of positive periodic solution for the corresponding periodic system are obtained by using the fixed point theory and some new analysis techniques. In additional, some numerical solutions of the equations describing the system are given to verify the obtained criteria are new, general, and easily verifiable. Finally, we still solve numerically the corresponding stochastic predator-prey models with multiplicative noise sources, and obtain some new interesting dynamical behaviors of the system.

关键词: predator-prey model, delay, diffusion, permanence, attractivity, periodic solution

Abstract: This article is focusing on a class of multi-delay predator-prey model with feedback controls and prey diffusion. By developing some new analysis methods and using the theory of differential inequalities as well as constructing a suitable Lyapunov function, we establish a set of easily verifiable sufficient conditions which guarantee the permanence of the system and the globally attractivity of positive solution for the predator-prey system. Furthermore, some conditions for the existence, uniqueness and stability of positive periodic solution for the corresponding periodic system are obtained by using the fixed point theory and some new analysis techniques. In additional, some numerical solutions of the equations describing the system are given to verify the obtained criteria are new, general, and easily verifiable. Finally, we still solve numerically the corresponding stochastic predator-prey models with multiplicative noise sources, and obtain some new interesting dynamical behaviors of the system.

Key words: predator-prey model, delay, diffusion, permanence, attractivity, periodic solution