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International Journal of Nonlinear Sciences and Numerical Simulation

Editor-in-Chief: Birnir, Björn

Editorial Board: Angheluta-Bauer, Luiza / Chen, Xi / Chou, Tom / Grauer, Rainer / Marzocchella, Antonio / Rangarajan, Govindan / Trivisa, Konstantina / Weikard, Rudi / Yang, Xu

IMPACT FACTOR 2017: 1.162

CiteScore 2018: 1.11

SCImago Journal Rank (SJR) 2018: 0.288
Source Normalized Impact per Paper (SNIP) 2018: 0.510

Mathematical Citation Quotient (MCQ) 2017: 0.12

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Volume 20, Issue 2


Dynamical Behaviors of a Fractional-Order Predator–Prey Model with Holling Type IV Functional Response and Its Discretization

A. M. Yousef / S. Z. Rida / Y. Gh. Gouda / A. S. Zaki
Published Online: 2019-01-26 | DOI: https://doi.org/10.1515/ijnsns-2017-0152


In this paper, we investigate the dynamical behaviors of a fractional-order predator–prey with Holling type IV functional response and its discretized counterpart. First, we seek the local stability of equilibria for the fractional-order model. Also, the necessary and sufficient conditions of the stability of the discretized model are achieved. Bifurcation types (include transcritical, flip and Neimark–Sacker) and chaos are discussed in the discretized system. Finally, numerical simulations are executed to assure the validity of the obtained theoretical results.

Keywords: predator–prey system; fractional calculus,discretization; functional response; bifurcations; chaos

MSC 2010: 26A33; 34C23; 37D45


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About the article

Received: 2017-07-09

Accepted: 2019-12-01

Published Online: 2019-01-26

Published in Print: 2019-04-26

Citation Information: International Journal of Nonlinear Sciences and Numerical Simulation, Volume 20, Issue 2, Pages 125–136, ISSN (Online) 2191-0294, ISSN (Print) 1565-1339, DOI: https://doi.org/10.1515/ijnsns-2017-0152.

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