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Volume 7, Issue 1
Chaos Control and Behavior Analysis of a Discrete-Time Dynamical System with Competitive Effect

Xiongxiong Du, Xiaoling Han & Ceyu Lei

DOI: 10.12150/jnma.2025.43

J. Nonl. Mod. Anal., 7 (2025), pp. 43-61.

Published online: 2025-02

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

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  • Abstract

This paper is about a class of discrete-time dynamical systems with competitive effects. The local stability of the positive equilibrium point of the system and the conditions for the existence of flip bifurcation and Neimark-Sacker bifurcation are discussed by using the center manifold theorem and bifurcation theory. In addition, the direction of the flip bifurcation and Neimark-Sacker bifurcation is given. Furthermore, a feedback control strategy is employed to control bifurcation and chaos in the system. Finally, flip bifurcation, Neimark-Sacker bifurcation and chaos control strategy are verified with the help of numerical simulations.

  • Keywords

Predator-prey system, flip bifurcation, Neimark-Sacker bifurcation, competitive effect, chaos.

  • AMS Subject Headings

37N25, 39A28, 39A30, 92D25

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{JNMA-7-43, author = {Du , XiongxiongHan , Xiaoling and Lei , Ceyu}, title = {Chaos Control and Behavior Analysis of a Discrete-Time Dynamical System with Competitive Effect}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2025}, volume = {7}, number = {1}, pages = {43--61}, abstract = {

This paper is about a class of discrete-time dynamical systems with competitive effects. The local stability of the positive equilibrium point of the system and the conditions for the existence of flip bifurcation and Neimark-Sacker bifurcation are discussed by using the center manifold theorem and bifurcation theory. In addition, the direction of the flip bifurcation and Neimark-Sacker bifurcation is given. Furthermore, a feedback control strategy is employed to control bifurcation and chaos in the system. Finally, flip bifurcation, Neimark-Sacker bifurcation and chaos control strategy are verified with the help of numerical simulations.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2025.43}, url = {http://global-sci.org/intro/article_detail/jnma/23832.html} }
TY - JOUR T1 - Chaos Control and Behavior Analysis of a Discrete-Time Dynamical System with Competitive Effect AU - Du , Xiongxiong AU - Han , Xiaoling AU - Lei , Ceyu JO - Journal of Nonlinear Modeling and Analysis VL - 1 SP - 43 EP - 61 PY - 2025 DA - 2025/02 SN - 7 DO - http://doi.org/10.12150/jnma.2025.43 UR - https://global-sci.org/intro/article_detail/jnma/23832.html KW - Predator-prey system, flip bifurcation, Neimark-Sacker bifurcation, competitive effect, chaos. AB -

This paper is about a class of discrete-time dynamical systems with competitive effects. The local stability of the positive equilibrium point of the system and the conditions for the existence of flip bifurcation and Neimark-Sacker bifurcation are discussed by using the center manifold theorem and bifurcation theory. In addition, the direction of the flip bifurcation and Neimark-Sacker bifurcation is given. Furthermore, a feedback control strategy is employed to control bifurcation and chaos in the system. Finally, flip bifurcation, Neimark-Sacker bifurcation and chaos control strategy are verified with the help of numerical simulations.

Du , XiongxiongHan , Xiaoling and Lei , Ceyu. (2025). Chaos Control and Behavior Analysis of a Discrete-Time Dynamical System with Competitive Effect. Journal of Nonlinear Modeling and Analysis. 7 (1). 43-61. doi:10.12150/jnma.2025.43
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