Stability, bifurcation and chaos control of a discretized Leslie prey-predator model

•A non-standard finite difference scheme is used to discretize a continuous-time Leslie prey-predator model.•The local stability of the fixed points and Neimark-Sacker bifurcation at the positive fixed point was determined.•Hybrid control technique is used to control bifurcation in the model at the...

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Published in:Chaos, solitons and fractals solitons and fractals, 2021-11, Vol.152, p.111345, Article 111345
Main Authors: Akhtar, S., Ahmed, R., Batool, M., Shah, Nehad Ali, Chung, Jae Dong
Format: Article
Language:English
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Summary:•A non-standard finite difference scheme is used to discretize a continuous-time Leslie prey-predator model.•The local stability of the fixed points and Neimark-Sacker bifurcation at the positive fixed point was determined.•Hybrid control technique is used to control bifurcation in the model at the positive fixed point.•Hybrid control technique is used to control chaos in the model at the positive fixed point. For a variety of purposes, discrete-time models are superior to continuous-time models. Many techniques are introduced to discretize continuous-time models. In this paper, a non-standard finite difference scheme is used to discretize a continuous-time Leslie prey-predator model. We study the local stability of the fixed points and Neimark-Sacker bifurcation at the positive fixed point. Moreover, hybrid control technique is used to control chaos and bifurcation in the model at the positive fixed point. Numerical simulations are provided to illustrate the theoretical discussion.
ISSN:0960-0779
1873-2887
DOI:10.1016/j.chaos.2021.111345