Open AccessStability and Anti-Chaos Control of Discrete Quadratic Maps
Author(s) -
Sarbast H. Mikaeel,
A. George Maria Selvam,
D. Vignesh,
Bewar Beshay
Publication year - 2021
Publication title -
iraqi journal of science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.152
H-Index - 4
eISSN - 2312-1637
pISSN - 0067-2904
DOI - 10.24996/ijs.2021.62.5.30
Subject(s) - dynamical systems theory , chaotic , quadratic equation , stability (learning theory) , dynamical system (definition) , mathematics , nonlinear system , control of chaos , statistical physics , differential equation , control theory (sociology) , computer science , synchronization of chaos , mathematical analysis , control (management) , physics , geometry , quantum mechanics , artificial intelligence , machine learning
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.