Chaos and bifurcation of discontinuous dynamical systems with piecewise constant arguments

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

Chaos and bifurcation of discontinuous dynamical systems with piecewise constant arguments

Authors :

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

Author Address :

^aFaculty of Science, Alexandria University, Alexandria, Egypt.
^bFaculty of Education, 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 a discontinuous dynamical system of the Riccati type 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 system of the Riccati type equation.

Keywords :

Discontinuous dynamical systems, piecewise constant arguments, Riccati type equation, fixed points, bifurcation, chaos.

DOI :

Article Info :

Received : August 28, 2012; Accepted : September 04, 2012.