Stability and Anti-Chaos Control of Discrete Quadratic Maps

Abstract

A dynamical system describes the consequence of the current state of an event or particle in future. The models expressed by functions in the dynamical systems are more often deterministic, but these functions might also be stochastic in some cases. The prediction of the system's behavior in future is studied with the analytical solution of the implicit relations (Differential, Difference equations) and simulations. A discrete-time first order system of equations with quadratic nonlinearity is considered for study in this work. Classical approach of stability analysis using Jury's condition is employed to analyze the system's stability. The chaotic nature of the dynamical system is illustrated by the bifurcation theory. The enhancement of chaos is performed using Cosine Chaotification Technique (CCT).
 Simulations are carried out for different parameter values.