Chaos and bifurcation of the Logistic discontinuous dynamical systems with piecewise constant arguments

A.M.A. El-Sayeda,* and S.M. Salmanb

Chaos and bifurcation of the Logistic discontinuous dynamical systems with piecewise constant arguments

Authors :

A.M.A. El-Sayed^a,* and S.M. Salman^b

Author Address :

^a,bFaculty of Science, Alexandria University, Alexandria, Egypt.

*Corresponding author.

Abstract :

In this paper we are concerned with the definition and some properties of the discontinuous dynamical systems generated by piecewise constant arguments. Then we study two discontinuous dynamical system of the Logistic equation as an example. The local stability at the fixed points is studied. The bifurcation analysis and chaos are discussed. In addition, we compare our results with the discrete dynamical systems of the Logistic equation.

Keywords :

Discontinuous dynamical systems, piecewise constant argument, Logistic equation, fixed points, bifurcation, chaos.

DOI :

Article Info :

Received : January 22, 2013; Accepted : April 17, 2013.