Parametric effect on discrete dynamic systems causing of chaos and dispersion

Abstract

In the past the logistic equation where applied to real numbers and produes no dispersion and chaos, in this paper, we present the equivalent system of complex logistic equation. We will study parametric behavior on discrete dynamic system of complex variable, and study some dynamic properties such as fixed points and their asymptotic stability, Lyapunov exponents, chaos and bifurcation. Numerical results which confirm the theoretical analysis are presented. It is noted that dispersion and chaos have accured. We have used AL-Matlab to clarify the bifurcation diagrams and chaos both in 2D and 3D.
Keywords: logistic equation, fixed points, stability, Lyapunov exponent, bifurcation, chaos, chaotic attractor.