GLOBAL STABILITY OF PERIODIC SOLUTIONS OF PREDATOR-PREY SYSTEM WITH HOLLING TYPE Ⅲ FUNCTIONAL RESPONSE

Xiang Zhu; Wei Ding

doi:10.11948/2156-907X.20190121

2019 Volume 9 Issue 4

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Xiang Zhu, Wei Ding. GLOBAL STABILITY OF PERIODIC SOLUTIONS OF PREDATOR-PREY SYSTEM WITH HOLLING TYPE Ⅲ FUNCTIONAL RESPONSE[J]. Journal of Applied Analysis & Computation, 2019, 9(4): 1606-1615. doi: 10.11948/2156-907X.20190121

Citation:

Xiang Zhu, Wei Ding. GLOBAL STABILITY OF PERIODIC SOLUTIONS OF PREDATOR-PREY SYSTEM WITH HOLLING TYPE Ⅲ FUNCTIONAL RESPONSE[J]. Journal of Applied Analysis & Computation, 2019, 9(4): 1606-1615. doi: 10.11948/2156-907X.20190121

GLOBAL STABILITY OF PERIODIC SOLUTIONS OF PREDATOR-PREY SYSTEM WITH HOLLING TYPE Ⅲ FUNCTIONAL RESPONSE

Xiang Zhu¹,
Wei Ding^1, ,

1.
Department of Mathematic, Shanghai Normal University, 100 Guilin Road, 200234, China

Corresponding author: Email address:dingwei@shnu.edu.cn(W. Ding)

Abstract

Abstract

This paper studied some properties of a predator-prey system with Holling type Ⅲ functional response. Based on Mawhin's Continuation Theorem, some sufficient conditions for the existence of periodic solutions are obtained. Moreover, the global stability of the periodic solution is built with the help of a suitable Lyapunov function.
- Periodic solution /
- Mawhin's Continuous Theorem /
- global stability /
- Lyapunov function
MSC: 34C25, 34D23

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References

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