Adaptive Synchronization between Two Delayed Chaotic Systems Based on Parameter Identification

2008 ◽  
Author(s):  
Lidan Wang ◽  
Shukai Duan
Keyword(s):  
Parameter Identification ◽  
Chaotic Systems ◽  
Adaptive Synchronization

Dynamics, Synchronization and Electronic Implementations of a New Lorenz-like Chaotic System with Nonhyperbolic Equilibria

2019 ◽  
Vol 29 (14) ◽  
pp. 1950197 ◽  
Author(s):  
P. D. Kamdem Kuate ◽  
Qiang Lai ◽  
Hilaire Fotsin
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Chaotic Behavior ◽  
Piecewise Linear ◽  
Period Doubling ◽  
Adaptive Synchronization ◽  
The Novel ◽  
Algebraic Equations ◽  
The Lorenz System

The Lorenz system has attracted increasing attention on the issue of its simplification in order to produce the simplest three-dimensional chaotic systems suitable for secure information processing. Meanwhile, Sprott’s work on elegant chaos has revealed a set of 19 chaotic systems all described by simple algebraic equations. This paper presents a new piecewise-linear chaotic system emerging from the simplification of the Lorenz system combined with the elegance of Sprott systems. Unlike the majority, the new system is a non-Shilnikov chaotic system with two nonhyperbolic equilibria. It is multiplier-free, variable-boostable and exclusively based on absolute value and signum nonlinearities. The use of familiar tools such as Lyapunov exponents spectra, bifurcation diagrams, frequency power spectra as well as Poincaré map help to demonstrate its chaotic behavior. The novel system exhibits inverse period doubling bifurcations and multistability. It has only five terms, one bifurcation parameter and a total amplitude controller. These features allow a simple and low cost electronic implementation. The adaptive synchronization of the novel system is investigated and the corresponding electronic circuit is presented to confirm its feasibility.

Robust Adaptive Synchronization of Chaotic Systems With Nonsymmetric Input Saturation Constraints

2017 ◽  
Vol 13 (1) ◽  
Author(s):  
Samaneh Mohammadpour ◽  
Tahereh Binazadeh
Keyword(s):  
Chaotic Systems ◽  
Sliding Mode ◽  
Input Saturation ◽  
Adaptive Synchronization ◽  
Adaptive Sliding Mode Controller ◽  
Robust Synchronization ◽  
Effective Performance ◽  
Saturation Constraints ◽  
Robust Adaptive ◽  
Input Saturation Constraints

This paper considers the robust synchronization of chaotic systems in the presence of nonsymmetric input saturation constraints. The synchronization happens between two nonlinear master and slave systems in the face of model uncertainties and external disturbances. A new adaptive sliding mode controller is designed in a way that the robust synchronization occurs. In this regard, a theorem is proposed, and according to the Lyapunov approach the adaptation laws are derived, and it is proved that the synchronization error converges to zero despite of the uncertain terms in master and slave systems and nonsymmetric input saturation constraints. Finally, the proposed method is applied on chaotic gyro systems to show its applicability. Computer simulations verify the theoretical results and also show the effective performance of the proposed controller.

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