Dynamical Properties of a Herbivore-Plankton Impulsive Semidynamic System with Eating Behavior

Yufei Wang,Qingjian Li,Huidong Cheng

doi:10.1155/2020/5726895

Abstract

In this paper, an impulsive semidynamic system of the relationship between plankton and herbivore is established, and the Poincaré map method is used to extend the new properties of the model. We define the Poincaré map of the impulsive point series in phase concentration and analyze the characteristics. A comprehensive and detailed analysis of the periodic solution is performed. In addition, the numerical simulations illustrate the correctness of our arguments. The results show that plankton and herbivore can survive stably under effective control.

Highlights

In terrestrial and aquatic ecosystems, the energy conversion and nutrient cycle between plankton and herbivores play an important role [1]
Sharma et al [6] put forward a predator model of plankton and herbivores, made a qualitative analysis of the model system, discussed the stability of the equilibrium point, and explored ways to maintain the ecological balance of the population at different harvest levels
An impulsive semidynamic system of plankton and herbivore is established in this paper. e numerical simulation illustrates the correctness of our arguments

Summary

Introduction

In terrestrial and aquatic ecosystems, the energy conversion and nutrient cycle between plankton and herbivores play an important role [1]. In Zhong et al.’s paper [5], the interaction model of nutrient solution, plankton, and herbivores was established, and the limit cycle and other dynamic properties were studied. When the control parameters are changed, the global dynamics are not well processed; the periodic solutions of the model are not thoroughly studied; and the biological meanings of the complex dynamics are not well analyzed and revealed. In order to solve these problems, more advanced qualitative techniques and new methods are needed to reveal the complete dynamic properties and control strategies of biological dynamic systems. Erefore, we propose a herbivore-plankton pulse semidynamic system, which uses the Poincaremap method to comprehensively analyze and study the complex dynamics of the model.

Preliminaries

Herbivore-Plankton Interaction Model and Its Properties

Poincare Map and Its Main Properties

Periodic Solution of the System

Numerical Simulations

Conclusion