The dynamic behaviors of a new impulsive predator prey model with impulsive control at different fixed moments

Lin Jun Wang; You Xiang Xie; Qi Cheng Deng

Kybernetika (2018)

  • Volume: 54, Issue: 3, page 522-541
  • ISSN: 0023-5954

Abstract

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In this paper, we propose a new impulsive predator prey model with impulsive control at different fixed moments and analyze its interesting dynamic behaviors. Sufficient conditions for the globally asymptotical stability of the semi-trivial periodic solution and the permanence of the present model are obtained by Floquet theory of impulsive differential equation and small amplitude perturbation skills. Existences of the "infection-free" periodic solution and the "predator-free" solution are analyzed by bifurcation theory of impulsive differential equation. Finally, the analytical results presented in the work are validated by numerical simulation figures for this proposed model.

How to cite

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Wang, Lin Jun, Xie, You Xiang, and Deng, Qi Cheng. "The dynamic behaviors of a new impulsive predator prey model with impulsive control at different fixed moments." Kybernetika 54.3 (2018): 522-541. <http://eudml.org/doc/294815>.

@article{Wang2018,
abstract = {In this paper, we propose a new impulsive predator prey model with impulsive control at different fixed moments and analyze its interesting dynamic behaviors. Sufficient conditions for the globally asymptotical stability of the semi-trivial periodic solution and the permanence of the present model are obtained by Floquet theory of impulsive differential equation and small amplitude perturbation skills. Existences of the "infection-free" periodic solution and the "predator-free" solution are analyzed by bifurcation theory of impulsive differential equation. Finally, the analytical results presented in the work are validated by numerical simulation figures for this proposed model.},
author = {Wang, Lin Jun, Xie, You Xiang, Deng, Qi Cheng},
journal = {Kybernetika},
keywords = {impulsive differential equation; bifurcation theory; stability; impulsive control; persistence and extinction},
language = {eng},
number = {3},
pages = {522-541},
publisher = {Institute of Information Theory and Automation AS CR},
title = {The dynamic behaviors of a new impulsive predator prey model with impulsive control at different fixed moments},
url = {http://eudml.org/doc/294815},
volume = {54},
year = {2018},
}

TY - JOUR
AU - Wang, Lin Jun
AU - Xie, You Xiang
AU - Deng, Qi Cheng
TI - The dynamic behaviors of a new impulsive predator prey model with impulsive control at different fixed moments
JO - Kybernetika
PY - 2018
PB - Institute of Information Theory and Automation AS CR
VL - 54
IS - 3
SP - 522
EP - 541
AB - In this paper, we propose a new impulsive predator prey model with impulsive control at different fixed moments and analyze its interesting dynamic behaviors. Sufficient conditions for the globally asymptotical stability of the semi-trivial periodic solution and the permanence of the present model are obtained by Floquet theory of impulsive differential equation and small amplitude perturbation skills. Existences of the "infection-free" periodic solution and the "predator-free" solution are analyzed by bifurcation theory of impulsive differential equation. Finally, the analytical results presented in the work are validated by numerical simulation figures for this proposed model.
LA - eng
KW - impulsive differential equation; bifurcation theory; stability; impulsive control; persistence and extinction
UR - http://eudml.org/doc/294815
ER -

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