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Journal of Applied Mathematics and Computation

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ArticleOpen Access http://dx.doi.org/10.26855/jamc.2022.12.008

Study on Predator-Prey System with Impulsive Release of Predator Population in Polluted Water

Xiuxiu Wang, Meng Zhang*

School of Science, Beijing University of Civil Engineering and Architecture, Beijing, China.

*Corresponding author: Meng Zhang

Published: December 21,2022

Abstract

The phenomenon of destroying aquatic ecosystems caused by eutrophication of water occurs from time to time. This paper proposes a prey-predator system with impulsive release of predator populations in polluted water. By constructing Lyapunov function, a sufficient condition for the global asymptotic stability of the system without impulsive effect is obtained. Then, by using the geometric theory of semi-continuous dynamical systems and the successor function method, the existence and uniqueness of the order-1 periodic solution are analyzed, and the stability of the order-1 periodic solution is discussed by using the Analogue of the Poincaré criterion of impulsive differential equations. Finally, we illustrate our theoretical results and biological significance by numerical simulation.

Keywords

Polluted Water, Impulsive Release, Semicontinuous Dynamical System, Order-1 Periodic Solution, Successor Function

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How to cite this paper

Study on Predator-Prey System with Impulsive Release of Predator Population in Polluted Water

How to cite this paper:  Xiuxiu Wang, Meng Zhang. (2022) Study on Predator-Prey System with Impulsive Release of Predator Population in Polluted Water. Journal of Applied Mathematics and Computation6(4), 458-471.

DOI: http://dx.doi.org/10.26855/jamc.2022.12.008