Chaotic Dynamics and Control of Discrete Ratio-Dependent Predator-Prey System

Sarker Md. Sohel Rana

Discrete Dynamics in Nature and Society, 2017, vol. 2017, 1-13

Abstract:

This study examines the complexity of a discrete-time predator-prey system with ratio-dependent functional response. We establish algebraically the conditions for existence of fixed points and their stability. We show that under some parametric conditions the system passes through a bifurcation (flip or Neimark-Sacker). Numerical simulations are presented not only to justify theoretical results but also to exhibit new complex behaviors which include phase portraits, orbits of periods 9, 19, and 26, invariant closed circle, and attracting chaotic sets. Moreover, we measure numerically the Lyapunov exponents and fractal dimension to confirm the chaotic dynamics of the system. Finally, a state feedback control method is applied to control chaos which exists in the system.

Date: 2017
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/DDNS/2017/4537450.pdf (application/pdf)
http://downloads.hindawi.com/journals/DDNS/2017/4537450.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:jnddns:4537450

DOI: 10.1155/2017/4537450

Access Statistics for this article

More articles in Discrete Dynamics in Nature and Society from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().