On a New Three-Dimensional Chaotic System with Adaptive Control and Chaos Synchronization

A three-dimensional autonomous deterministic chaotic system having six parameters is explored within this article. The dynamical characteristics of the proposed system are investigated through eigenvalues structure, bifurcation diagrams, Kaplan–Yorke dimension, Lyapunov exponents, time response, and...

Full description

Saved in:
Bibliographic Details
Published in:Shock and vibration 2023-04, Vol.2023, p.1-19
Main Authors: Saeed, Nasser A., Saleh, Hend A., El-Ganaini, Wedad A., Kamel, Magdi, Mohamed, Mohamed S.
Format: Article
Language:English
Subjects:
Adaptive control
Adaptive systems
Chaos theory
Circuits
Coefficient of variation
Computer science
Computer systems
Control theory
Cryptography
Design parameters
Dynamical systems
Eigenvalues
Electronic circuits
Equilibrium
Image processing
Liapunov exponents
Microelectromechanical systems
Orbits
Oscillations
Simulation methods
Synchronism
Time response
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:A three-dimensional autonomous deterministic chaotic system having six parameters is explored within this article. The dynamical characteristics of the proposed system are investigated through eigenvalues structure, bifurcation diagrams, Kaplan–Yorke dimension, Lyapunov exponents, time response, and phase plane trajectories. For the suitable design of the system parameters, it is found that the system can exhibit periodic, period-n, or chaotic oscillations. Accordingly, the system’s dynamical behavior to the variation of its coefficients has been explored. The obtained results revealed that the proposed dynamical system does not lose its chaotic oscillations for the small fluctuations of one or more of the values of its parameters. In addition, chaos control and chaos synchronization have been studied by means of the adaptive control strategy relying on Lyapunov’s second method of stability. The numerical simulation revealed that superior chaos control and master-slave synchronization have been achieved by the applied control laws. Finally, the obtained results have been simulated via a nonlinear electronic circuit that demonstrated the feasibility of the purposed chaotic system for different engineering applications such as secure communications, cryptosystems, image encryption, and image processing.
ISSN:1070-9622
1875-9203
DOI:10.1155/2023/1969500