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Discrete Dynamics in Nature and Society
Volume 2017 (2017), Article ID 9705985, 11 pages
https://doi.org/10.1155/2017/9705985
Research Article

Bifurcation Analysis and Chaos Control in a Discrete-Time Predator-Prey System of Leslie Type with Simplified Holling Type IV Functional Response

1Department of Mathematics, University of Dhaka, Dhaka 1000, Bangladesh
2Department of Computer Science and Engineering, University of Asia Pacific, Dhaka 1215, Bangladesh

Correspondence should be addressed to S. M. Sohel Rana; moc.liamg@udhtm.anars

Received 30 March 2017; Accepted 4 June 2017; Published 25 July 2017

Academic Editor: Qamar Din

Copyright © 2017 S. M. Sohel Rana and Umme Kulsum. 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.

Abstract

The dynamic behavior of a discrete-time predator-prey system of Leslie type with simplified Holling type IV functional response is examined. We algebraically show that the system undergoes a bifurcation (flip or Neimark-Sacker) in the interior of . Numerical simulations are presented not only to validate analytical results but also to show chaotic behaviors which include bifurcations, phase portraits, period 2, 4, 6, 8, 10, and 20 orbits, invariant closed cycle, and attracting chaotic sets. Furthermore, we compute numerically maximum Lyapunov exponents and fractal dimension to justify the chaotic behaviors of the system. Finally, a strategy of feedback control is applied to stabilize chaos existing in the system.