Abstract

Water hyacinth and its ecological invasion have negative impacts on diversity of indigenous species and ecosystems, which becomes one of the hotspots in current ecological research. In this paper, a water hyacinth ecological system with two state‐dependent impulse controls is studied. Firstly, we define the successor functions of semicontinuous dynamic system and give existence theorems of order‐1 periodic solution and order‐2 periodic solution of such system. Secondly, we analyze singular points of the system without impulsive state feedback control qualitatively and get the condition for focus point. Thirdly, we obtain the sufficient condition under which the system has an order‐1 or order‐2 periodic solution through the method of successor function and prove the stability of the order‐1 or order‐2 periodic solution by the analogue of Poincaré’s criterion. Furthermore, some examples and numerical simulations are given to illustrate our results.

Highlights

  • The water hyacinth, a water plant with a showy purple flower, is a native of the Amazon Basin and is treated as the most important nuisance aquatic plant worldwide

  • Nie et al [16,17,18] and Tian et al [19] put forward a class of predatorprey models with state-dependent impulsive effects

  • Zhao et al [20] using successor functions and Poincaré-Bendixson theorem of impulsive differential equations studied the existence of Complexity periodical solutions to a predator-prey model with two state impulses

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Summary

Introduction

The water hyacinth, a water plant with a showy purple flower, is a native of the Amazon Basin and is treated as the most important nuisance aquatic plant worldwide. Nie et al [16,17,18] and Tian et al [19] put forward a class of predatorprey models with state-dependent impulsive effects. Zhao et al [20] using successor functions and Poincaré-Bendixson theorem of impulsive differential equations studied the existence of Complexity periodical solutions to a predator-prey model with two state impulses. A water hyacinth ecological system with Kuznets curve effect and two state-dependent impulse controls is put forward and numerical simulations are carried out based on the qualitative analysis on the proposed model.

Model Formulation and Preliminaries
Model Analysis
D2 D D1 h2
Numerical Simulations and Discussion
F9 E2 F0
Conclusions
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