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Volume 2, Issue 2
Homoclinic Cycle and Homoclinic Bifurcations of a Predator-Prey Model with Impulsive State Feedback Control

Tongqian Zhang, Tong Xu, Junling Wang & Zhichao Jiang

DOI: 10.12150/jnma.2020.227

J. Nonl. Mod. Anal., 2 (2020), pp. 227-240.

Published online: 2021-04

[An open-access article; the PDF is free to any online user.]

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  • Abstract

In this paper, the homoclinic bifurcation of a predator-prey system with impulsive state feedback control is investigated. By using the geometry theory of semi-continuous dynamic systems, the existences of order-1 homoclinic cycle and order-1 periodic solution are obtained. Then the stability of order-1 periodic solution is studied. At last, an example is presented to illustrate the main results.

  • Keywords

Semi-continuous dynamic system, Successor function, Order-1 homoclinic cycle, Homoclinic bifurcation, Order-1 periodic solution.

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COPYRIGHT: © Global Science Press

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@Article{JNMA-2-227, author = {Zhang , TongqianXu , TongWang , Junling and Jiang , Zhichao}, title = {Homoclinic Cycle and Homoclinic Bifurcations of a Predator-Prey Model with Impulsive State Feedback Control}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2021}, volume = {2}, number = {2}, pages = {227--240}, abstract = {

In this paper, the homoclinic bifurcation of a predator-prey system with impulsive state feedback control is investigated. By using the geometry theory of semi-continuous dynamic systems, the existences of order-1 homoclinic cycle and order-1 periodic solution are obtained. Then the stability of order-1 periodic solution is studied. At last, an example is presented to illustrate the main results.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2020.227}, url = {http://global-sci.org/intro/article_detail/jnma/18808.html} }
TY - JOUR T1 - Homoclinic Cycle and Homoclinic Bifurcations of a Predator-Prey Model with Impulsive State Feedback Control AU - Zhang , Tongqian AU - Xu , Tong AU - Wang , Junling AU - Jiang , Zhichao JO - Journal of Nonlinear Modeling and Analysis VL - 2 SP - 227 EP - 240 PY - 2021 DA - 2021/04 SN - 2 DO - http://doi.org/10.12150/jnma.2020.227 UR - https://global-sci.org/intro/article_detail/jnma/18808.html KW - Semi-continuous dynamic system, Successor function, Order-1 homoclinic cycle, Homoclinic bifurcation, Order-1 periodic solution. AB -

In this paper, the homoclinic bifurcation of a predator-prey system with impulsive state feedback control is investigated. By using the geometry theory of semi-continuous dynamic systems, the existences of order-1 homoclinic cycle and order-1 periodic solution are obtained. Then the stability of order-1 periodic solution is studied. At last, an example is presented to illustrate the main results.

Zhang , TongqianXu , TongWang , Junling and Jiang , Zhichao. (2021). Homoclinic Cycle and Homoclinic Bifurcations of a Predator-Prey Model with Impulsive State Feedback Control. Journal of Nonlinear Modeling and Analysis. 2 (2). 227-240. doi:10.12150/jnma.2020.227
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