Chaotic dynamics of a discrete prey–predator model with Holling type II

A discrete-time prey–predator model with Holling type II is investigated. For this model, the existence and stability of three fixed points are analyzed. The bifurcation diagrams, phase portraits and Lyapunov exponents are obtained for different parameters of the model. The fractal dimension of a st...

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Bibliographic Details
Published inNonlinear analysis: real world applications Vol. 10; no. 1; pp. 116 - 129
Main Authors Agiza, H.N., ELabbasy, E.M., EL-Metwally, H., Elsadany, A.A.
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.02.2009
Subjects
Chaotic behavior
Fractal dimension
Holling type II functional response
Layapunov exponents
Prey–predator model
Prey–predator model
Fractal dimension
Holling type II functional response
Chaotic behavior
Layapunov exponents
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Summary:A discrete-time prey–predator model with Holling type II is investigated. For this model, the existence and stability of three fixed points are analyzed. The bifurcation diagrams, phase portraits and Lyapunov exponents are obtained for different parameters of the model. The fractal dimension of a strange attractor of the model was also calculated. Numerical simulations show that the discrete model exhibits rich dynamics compared with the continuous model, which means that the present model is a chaotic, and complex one.
ISSN:1468-1218
1878-5719
DOI:10.1016/j.nonrwa.2007.08.029