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Discrete Dynamics in Nature and Society
Volume 2017, Article ID 4537450, 13 pages
Research Article

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

Department of Mathematics, University of Dhaka, Dhaka 1000, Bangladesh

Correspondence should be addressed to Sarker Md. Sohel Rana; moc.liamg@udhtm.anars

Received 30 March 2017; Revised 8 May 2017; Accepted 15 May 2017; Published 10 July 2017

Academic Editor: Abdelalim Elsadany

Copyright © 2017 Sarker Md. Sohel Rana. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.