IJPAM: Volume 109, No. 2 (2016)

CONTROLLING CHAOTIC DYNAMICS OF
A CONTINUOUS ECOLOGICAL MODEL

Safaa Jawad Ali$^{1,2}$, Norihan Md. Arifin$^1$, Raid Kamel Naji$^3$,
Fudziah Ismail$^1$, Norfifah Bachok$^1$
$^1$Institute for Mathematical Research
University Putra Malaysia
MALAYSIA
$^2$Technical Instructor Preparing Institute
Middle Technical University
Baghdad, IRAQ
$^3$Department of Mathematics
College of Science
University of Baghdad
IRAQ


Abstract. In this paper a technique of controlling chaotic behavior of a three species food chain model with Sokol-Howell functional response by involving intraspecific competition is discussed. The model is proved to be dissipative in the positive octant. Controlling conditions of chaotic behavior of the system are carried out. Stability analysis of the equilibrium points is analyzed. Lyaponuv exponents and bifurcation diagrams are used to study the complex dynamics of the model. The impact of the intraspecific competition in the dynamics of the food chain model with Sokol-Howell response is investigated theoretically as well as numerically.

Received: March 2, 2016

AMS Subject Classification: 37D45, 37D50, 37C75

Key Words and Phrases: bifurcation diagram, chaotic, period doubling, Sokol-Howell response

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DOI: 10.12732/ijpam.v109i2.2 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 109
Issue: 2
Pages: 177 - 191


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