Acta mathematica scientia,Series A ›› 2018, Vol. 38 ›› Issue (5): 1001-1013.

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The Research on a Class of the Predator-Prey-Mutualist System with Delays

Lifei Zheng1(),Jie Guo1,Meihua Wu2,Xiaorui Wang1,Aying Wan2,*   

  1. 1 College of Science, Northwest A F University, Shaan'xi Yangling 712100
    2 College of Mathematics and Statistics, Hulunbuir Univeristy, Inner Mongolia Hailar 021008
  • Received:2017-03-08 Online:2018-11-09 Published:2018-11-09
  • Contact: Aying Wan E-mail:zhenglifei@nwsuaf.edu.cn
  • Supported by:
    the NSFC(11461024);the Science and Technology Bureau's Project of Hulunbeier City(9110/KY0156);the National Higher-Education Institution General Research and Development Project(2014YB023);the National Higher-Education Institution General Research and Development Project(2452015086);the National Higher-Education Institution General Research and Development Project(z109021561);the Supportive Subject Foundation of Shaanxi Province(14SXZD007)

Abstract:

In this paper, we establish a predator-prey-mutualist system with time delay, and the positive, persistence and local stability of the system are analyzed. The conclusion shows that it is possible that the system is stable, and the positive equilibrium point is asymptotically stable. Finally, numerical simulation with the relevant data in the ecosystem of ladybirds, cotton aphids and ants.The results show that development duration (time delay) of the prey and predator has an important influence on the whole system, and if growth duration is too long, the whole system will have periodic fluctuations.

Key words: Time Delay, Predator-prey-mutualist, Local Stability, Numerical modeling

CLC Number: 

  • O175
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