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Journal of Applied Mathematics and Computation

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Article Open 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.

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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