GLOBAL STABILITY OF PERIODIC SOLUTION FOR A 3-SPECIES NONAUTONOMOUS RATIO-DEPENDENT DIFFUSIVE PREDATOR-PREY SYSTEM

Lili Jia; Juan Huang; Changyou Wang

doi:10.11948/20230397

2024 Volume 14 Issue 4

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Article navigation > Journal of Applied Analysis & Computation > 2024 > 14(4): 2392-2410

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Lili Jia, Juan Huang, Changyou Wang. GLOBAL STABILITY OF PERIODIC SOLUTION FOR A 3-SPECIES NONAUTONOMOUS RATIO-DEPENDENT DIFFUSIVE PREDATOR-PREY SYSTEM[J]. Journal of Applied Analysis & Computation, 2024, 14(4): 2392-2410. doi: 10.11948/20230397

Citation:

Lili Jia, Juan Huang, Changyou Wang. GLOBAL STABILITY OF PERIODIC SOLUTION FOR A 3-SPECIES NONAUTONOMOUS RATIO-DEPENDENT DIFFUSIVE PREDATOR-PREY SYSTEM[J]. Journal of Applied Analysis & Computation, 2024, 14(4): 2392-2410. doi: 10.11948/20230397

GLOBAL STABILITY OF PERIODIC SOLUTION FOR A 3-SPECIES NONAUTONOMOUS RATIO-DEPENDENT DIFFUSIVE PREDATOR-PREY SYSTEM

1.
School of Mathematical Sciences, and V. C. & V. R. Key Lab of Sichuan Province, Sichuan Normal University, Chengdu, Sichuan 610066, China
2.
Department of Basic Teaching, Dianchi College of Yunnan University, Kunming, Yunnan 650228, China
3.
College of Applied Mathematics, Chengdu University of Information Technology, Chengdu, Sichuan 610225, China

Author Bio: Email: lilijiadianchi@163.com(L. Jia); Email: hjmath@163.com(J. Huang)
Corresponding author: Email: wangchangyou417@163.com(C. Wang)

Abstract

Abstract

A 3-species nonautonomous ratio-dependent diffusive predator-prey system is considered in this article. Firstly, by utilizing a comparison principle and fixed point theorem, the existence of solution which is space homogenous strictly positive and periodic for the above system is obtained. And the obtained conditions ensuring the existence of solution can be very easily verified. At the same time, we develop some new analysis techniques as a byproduct. Furthermore, with the help of the upper and lower solutions (UALS) approach for the parabolic partial differential equations and Lyapunov theory, we aim at the globally asymptotically stability problems of the solutions, and some judgment criteria are achieved. Finally, we give some numerical simulations results which validate the theoretical findings of this article.
- Nonautonomous /
- reaction-diffusion /
- predator-prey /
- global stability /
- ratio-dependent
MSC: 39A10

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References

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