The global finite-time synchronization of a class of chaotic systems via the variable-substitution and feedback control

2021 ◽  
Author(s):  
Yun Chen ◽  
Yanyi Xu ◽  
Qian Lin
Keyword(s):  
Feedback Control ◽  
Finite Time ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Time Synchronization ◽  
Optimization Technique ◽  
Third Order ◽  
Variable Substitution ◽  
The Lorenz System ◽  
Synchronization Scheme

Abstract This paper deals with the global finite-time synchronization of a class of third-order chaotic systems with some intersecting nonlinearities, which cover many famous chaotic systems. First, a simple, continuous and dimension-reducible control by the name of the variable-substitution and feedback control is designed to construct a master–slave finite-time synchronization scheme. Then, a global finite-time synchronization criterion for the synchronization scheme is proven and the synchronization time is analytically estimated. Subsequently, the criterion and optimization technique are applied to the well-known brushless direct current motor (BLDCM) system and the classic Lorenz system, respectively, further obtaining some new optimized synchronization criteria in the form of algebra. Two numerical examples for the BLDCM system and a numerical example for the Lorenz system are simulated and analyzed to verify the effectiveness of the theoretical results obtained in this paper.

Hidden Chaotic Attractors and Synchronization for a New Fractional-Order Chaotic System

2019 ◽  
Vol 14 (8) ◽  
Author(s):  
Zuoxun Wang ◽  
Jiaxun Liu ◽  
Fangfang Zhang ◽  
Sen Leng
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Finite Time ◽  
Chaotic Systems ◽  
Time Synchronization ◽  
Chaotic Attractors ◽  
Finite Time Stability ◽  
Integer Order ◽  
Different Types ◽  
Synchronization Scheme

Although a large number of hidden chaotic attractors have been studied in recent years, most studies only refer to integer-order chaotic systems and neglect the relationships among chaotic attractors. In this paper, we first extend LE1 of sprott from integer-order chaotic systems to fractional-order chaotic systems, and we add two constant controllers which could produce a novel fractional-order chaotic system with hidden chaotic attractors. Second, we discuss its complicated dynamic characteristics with the help of projection pictures and bifurcation diagrams. The new fractional-order chaotic system can exhibit self-excited attractor and three different types of hidden attractors. Moreover, based on fractional-order finite time stability theory, we design finite time synchronization scheme of this new system. And combination synchronization of three fractional-order chaotic systems with hidden chaotic attractors is also derived. Finally, numerical simulations demonstrate the effectiveness of the proposed synchronization methods.

Global Lagged Finite-Time Synchronization of Two Chaotic Lur’e Systems Subject to Time Delay

2015 ◽  
Vol 25 (12) ◽  
pp. 1550161 ◽  
Author(s):  
Yun Chen ◽  
Xiaofeng Wu ◽  
Qian Lin
Keyword(s):  
Time Delay ◽  
Finite Time ◽  
Time Synchronization ◽  
Signal Transmission ◽  
Feedback Controller ◽  
Linear Matrix ◽  
Lur’E Systems ◽  
Chaotic Lur’E Systems ◽  
Variable Substitution ◽  
Synchronization Scheme

This paper investigates the global lagged finite-time synchronization of the master-slave Lur’e systems subject to time delay of signal transmission. By designing a variable-substitution and feedback controller, a master-slave finite-time synchronization scheme for the Lur’e systems with time delay is built up. Two delay-independent global lagged finite-time synchronization criteria are proved in the forms of linear matrix inequalities (LMIs), and the corresponding settling time of synchronization is analytically estimated. The obtained LMI criteria are applied to Chua’s oscillators, obtaining some easily implemented algebraic criteria under various single-variable-substitution and feedback controller, which are then optimized to improve their conservative property. Finally, several numerical examples are illustrated to verify the effectiveness of the optimized criteria.

Synchronization of Quadratic Chaotic Systems Based on Simultaneous Estimation of Nonlinear Dynamics

2018 ◽  
Vol 13 (8) ◽  
Author(s):  
Amin Zarei ◽  
Saeed Tavakoli
Keyword(s):  
Nonlinear Dynamics ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Simultaneous Estimation ◽  
Control Law ◽  
Adaptive Mechanism ◽  
Lyapunov Theorem ◽  
Unknown Parameters ◽  
The Lorenz System ◽  
Synchronization Scheme

To synchronize quadratic chaotic systems, a synchronization scheme based on simultaneous estimation of nonlinear dynamics (SEND) is presented in this paper. To estimate quadratic terms, a compensator including Jacobian matrices in the proposed master–slave schematic is considered. According to the proposed control law and Lyapunov theorem, the asymptotic convergence of synchronization error to zero is proved. To identify unknown parameters, an adaptive mechanism is also used. Finally, a number of numerical simulations are provided for the Lorenz system and a memristor-based chaotic system to verify the proposed method.

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.

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