Stability and Anti-Chaos Control of Discrete Quadratic Maps

Abstract

A dynamical system describes the consequence of the current state of an event orparticle in future. The models expressed by functions in the dynamical systems aremore 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 analyticalsolution of the implicit relations (Differential, Difference equations) andsimulations. A discrete-time first order system of equations with quadraticnonlinearity is considered for study in this work. Classical approach of stabilityanalysis using Jury's condition is employed to analyze the system's stability. Thechaotic nature of the dynamical system is illustrated by the bifurcation theory. Theenhancement of chaos is performed using Cosine Chaotification Technique (CCT).Simulations are carried out for different parameter values.