Neimark-Sacker Bifurcation and Chaos Control in a Fractional-Order Plant-Herbivore Model
Joint Authors
Khalil, Hammad
Din, Q.
Elsadany, A. A.
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-04-10
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Din, Q.& Elsadany, A. A.& Khalil, Hammad. 2017. Neimark-Sacker Bifurcation and Chaos Control in a Fractional-Order Plant-Herbivore Model. Discrete Dynamics in Nature and Society،Vol. 2017, no. 2017, pp.1-15.
https://search.emarefa.net/detail/BIM-1151644
Modern Language Association (MLA)
Din, Q.…[et al.]. Neimark-Sacker Bifurcation and Chaos Control in a Fractional-Order Plant-Herbivore Model. Discrete Dynamics in Nature and Society No. 2017 (2017), pp.1-15.
https://search.emarefa.net/detail/BIM-1151644
American Medical Association (AMA)
Din, Q.& Elsadany, A. A.& Khalil, Hammad. Neimark-Sacker Bifurcation and Chaos Control in a Fractional-Order Plant-Herbivore Model. Discrete Dynamics in Nature and Society. 2017. Vol. 2017, no. 2017, pp.1-15.
https://search.emarefa.net/detail/BIM-1151644
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1151644