Peer-Reviewed Article November 13, 2013
On a discretization process of fractional-order Logistic differential equation
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Published in: Journal of the Egyptian Mathematical Society
Publisher: Springer Science+Business Media • Egypt • 1110-256X
Abstract
In this work we introduce a discretization process to discretize fractional-order differential equations. First of all, we consider the fractional-order Logistic differential equation then, we consider the corresponding fractional-order Logistic differential equation with piecewise constant arguments and we apply the proposed discretization on it. The stability of the fixed points of the resultant dynamical system and the Lyapunov exponent are investigated. Finally, we study some dynamic behavior of the resultant systems such as bifurcation and chaos.