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

H. N. Agiza; E. M. ELabbasy; H. EL-Metwally; A. A. Elsadany

doi:10.1016/j.nonrwa.2007.08.029

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

H. N. Agiza
, E. M. ELabbasy
, H. EL-Metwally
, A. A. Elsadany

Mansoura University

Research output: Contribution to journal › Article › peer-review

226 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	116-129
Number of pages	14
Journal	Nonlinear Analysis: Real World Applications
Volume	10
Issue number	1
DOIs	https://doi.org/10.1016/j.nonrwa.2007.08.029
State	Published - Feb 2009
Externally published	Yes

Keywords

Chaotic behavior
Fractal dimension
Holling type II functional response
Layapunov exponents
Prey-predator model

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10.1016/j.nonrwa.2007.08.029

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title = "Chaotic dynamics of a discrete prey-predator model with Holling type II",

abstract = "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.",

keywords = "Chaotic behavior, Fractal dimension, Holling type II functional response, Layapunov exponents, Prey-predator model",

author = "Agiza, \{H. N.\} and ELabbasy, \{E. M.\} and H. EL-Metwally and Elsadany, \{A. A.\}",

year = "2009",

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AU - Agiza, H. N.

AU - ELabbasy, E. M.

AU - EL-Metwally, H.

AU - Elsadany, A. A.

PY - 2009/2

Y1 - 2009/2

N2 - 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.

AB - 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.

KW - Chaotic behavior

KW - Fractal dimension

KW - Holling type II functional response

KW - Layapunov exponents

KW - Prey-predator model

UR - https://www.scopus.com/pages/publications/50349084379

U2 - 10.1016/j.nonrwa.2007.08.029

DO - 10.1016/j.nonrwa.2007.08.029

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VL - 10

SP - 116

EP - 129

JO - Nonlinear Analysis: Real World Applications

JF - Nonlinear Analysis: Real World Applications

IS - 1

ER -

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

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Keywords

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