Acta Mathematica Scientia

, Volume 39, Issue 2, pp 429–448 | Cite as

On a Multi-Delay Lotka-Volterra Predator-Prey Model with Feedback Controls and Prey Diffusion

  • Changyou Wang
  • Nan LiEmail author
  • Yuqian Zhou
  • Xingcheng Pu
  • Rui Li


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 

2010 MR Subject Classification

34C25 34D23 34D45 37N25 


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Copyright information

© Wuhan Institute Physics and Mathematics, Chinese Academy of Sciences 2019

Authors and Affiliations

  • Changyou Wang
    • 1
  • Nan Li
    • 2
    Email author
  • Yuqian Zhou
    • 1
  • Xingcheng Pu
    • 3
  • Rui Li
    • 3
  1. 1.College of Applied MathematicsChengdu University of Information TechnologyChengduChina
  2. 2.Department of Applied MathematicsSouthwestern University of Finance and EconomicsChengduChina
  3. 3.College of AutomationChongqing University of Posts and TelecommunicationsChongqingChina

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