Discontinuous dynamical system represents the Logistic retarded functional equation with two different delays

A. M. A. El-Sayeda,* and M. E. Nasrb

Discontinuous dynamical system represents the Logistic retarded functional equation with two different delays

Authors :

A. M. A. El-Sayed^a,* and M. E. Nasr^b

Author Address :

^aDepartment of Mathematics, Faculty of Science, Alexandria University,Alexandria, Egypt
^bDepartment of Mathematics,Faculty of Science, Benha University, Benha 13518, Egypt.

*Corresponding author.

Abstract :

In this work we are concerned with the discontinuous dynamical system representing the problem of the logistic retarded functional equation with two di.erent delays,
\begin{align*}
x(t)&=\rho x(t-r_1)[1-x(t-r_2)],\quad t\in(0,T],
x(t)=x_0,\quad t\le 0.
\end{align*}
The existence of a unique solution $x\in L^1[0, T ]$ which is continuously dependence on the initial data, will be proved. The local stability at the equilibrium points will be studied. The bifurcation analysis and chaos will be discussed.

Keywords :

Logistic functional equation, existence, uniqueness, equilibrium points, local stability, Chaos and Bifurcation.

DOI :

Article Info :

Received : October 16, 2012; Accepted : January 12, 2013.