一类具有时滞的捕食者-猎物-共生者系统的研究

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 Wan^2,*

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

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

Lifei Zheng,Jie Guo,Meihua Wu,Xiaorui Wang,Aying Wan. The Research on a Class of the Predator-Prey-Mutualist System with Delays[J].Acta mathematica scientia,Series A, 2018, 38(5): 1001-1013.

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Figures/Tables 11

References 14

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

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