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Discrete Dynamics in Nature and Society
Volume 2017 (2017), Article ID 6312964, 15 pages
Research Article

Neimark-Sacker Bifurcation and Chaos Control in a Fractional-Order Plant-Herbivore Model

1Department of Mathematics, The University of Poonch Rawalakot, Rawalakot 12350, Pakistan
2Basic Science Department, Faculty of Computers and Informatics, Suez Canal University, New Campus, Ismailia 41522, Egypt
3Department of Mathematics, University of Education, Attock Campus, Lahore, Punjab, Pakistan

Correspondence should be addressed to Qamar Din

Received 14 November 2016; Accepted 27 February 2017; Published 10 April 2017

Academic Editor: Josef Diblik

Copyright © 2017 Qamar Din et al. 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 work is related to dynamics of a discrete-time 3-dimensional plant-herbivore model. We investigate existence and uniqueness of positive equilibrium and parametric conditions for local asymptotic stability of positive equilibrium point of this model. Moreover, it is also proved that the system undergoes Neimark-Sacker bifurcation for positive equilibrium with the help of an explicit criterion for Neimark-Sacker bifurcation. The chaos control in the model is discussed through implementation of two feedback control strategies, that is, pole-placement technique and hybrid control methodology. Finally, numerical simulations are provided to illustrate theoretical results. These results of numerical simulations demonstrate chaotic long-term behavior over a broad range of parameters. The computation of the maximum Lyapunov exponents confirms the presence of chaotic behavior in the model.