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Discrete-Time Predator-Prey Model with Bifurcations and Chaos
Joint Authors
Source
Mathematical Problems in Engineering
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-14, 14 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-11-16
Country of Publication
Egypt
No. of Pages
14
Main Subjects
Abstract EN
In this paper, local dynamics, bifurcations and chaos control in a discrete-time predator-prey model have been explored in ℝ+2.
It is proved that the model has a trivial fixed point for all parametric values and the unique positive fixed point under definite parametric conditions.
By the existing linear stability theory, we studied the topological classifications at fixed points.
It is explored that at trivial fixed point model does not undergo the flip bifurcation, but flip bifurcation occurs at the unique positive fixed point, and no other bifurcations occur at this point.
Numerical simulations are performed not only to demonstrate obtained theoretical results but also to tell the complex behaviors in orbits of period-4, period-6, period-8, period-12, period-17, and period-18.
We have computed the Maximum Lyapunov exponents as well as fractal dimension numerically to demonstrate the appearance of chaotic behaviors in the considered model.
Further feedback control method is employed to stabilize chaos existing in the model.
Finally, existence of periodic points at fixed points for the model is also explored.
American Psychological Association (APA)
Al-Basyouni, K. S.& Khan, A. Q.. 2020. Discrete-Time Predator-Prey Model with Bifurcations and Chaos. Mathematical Problems in Engineering،Vol. 2020, no. 2020, pp.1-14.
https://search.emarefa.net/detail/BIM-1201693
Modern Language Association (MLA)
Al-Basyouni, K. S.& Khan, A. Q.. Discrete-Time Predator-Prey Model with Bifurcations and Chaos. Mathematical Problems in Engineering No. 2020 (2020), pp.1-14.
https://search.emarefa.net/detail/BIM-1201693
American Medical Association (AMA)
Al-Basyouni, K. S.& Khan, A. Q.. Discrete-Time Predator-Prey Model with Bifurcations and Chaos. Mathematical Problems in Engineering. 2020. Vol. 2020, no. 2020, pp.1-14.
https://search.emarefa.net/detail/BIM-1201693
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1201693