Discrete-Time Predator-Prey Model with Bifurcations and Chaos

K. S. Al-Basyouni and A. Q. Khan

Mathematical Problems in Engineering, 2020, vol. 2020, 1-14

Abstract:

In this paper, local dynamics, bifurcations and chaos control in a discrete-time predator-prey model have been explored in . 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.

Date: 2020
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/MPE/2020/8845926.pdf (application/pdf)
http://downloads.hindawi.com/journals/MPE/2020/8845926.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:8845926

DOI: 10.1155/2020/8845926

Access Statistics for this article

More articles in Mathematical Problems in Engineering from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().