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.

scholarly journals Synchronization methods for chaotic systems involving fractional derivative with a non-singular kernel.

2020 ◽  
Author(s):  
Fatiha Mesdoui ◽  
Nabil Shawagfeh ◽  
Adel Ouannas
Keyword(s):  
Fractional Derivative ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Projective Synchronization ◽  
Singular Kernel ◽  
Lyapunov Theorem ◽  
Control Scheme ◽  
Different Dimensions ◽  
The Lorenz System ◽  
Liu System

This study considers the problem of control-synchronization for chaotic systems involving fractional derivative with a non-singular kernel. Using an extension of the Lyapunov Theorem for systems with Atangana-Baleanu-Caputo (ABC) derivative, a suitable control scheme is designed to achieve matrix projective synchronization (MP) between nonidentical ABC systems with different dimensions. The results are exemplified by the ABC version of the Lorenz system, Bloch system, and Liu system. To show the effectiveness of the proposed results, numerical simulations are performed based on the Adams-Bashforth-Mounlton numerical algorithm.

ANTICIPATED FUNCTION SYNCHRONIZATION WITH UNKNOWN PARAMETERS OF DISCRETE-TIME CHAOTIC SYSTEMS

2009 ◽  
Vol 20 (04) ◽  
pp. 597-608 ◽  
Author(s):  
YIN LI ◽  
BIAO LI ◽  
YONG CHEN
Keyword(s):  
Chaotic System ◽  
Discrete Time ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Control Law ◽  
Unknown Parameters ◽  
Synchronization Problem ◽  
Synchronization Scheme ◽  
Hyperchaotic Systems ◽  
Function Synchronization

In this paper, firstly, the control problem for the chaos synchronization of discrete-time chaotic (hyperchaotic) systems with unknown parameters are considered. Next, backstepping control law is derived to make the error signals between drive 2D discrete-time chaotic system and response 2D discrete-time chaotic system with two uncertain parameters asymptotically synchronized. Finally, the approach is extended to the synchronization problem for 3D discrete-time chaotic system with two unknown parameters. Numerical simulations are presented to show the effectiveness of the proposed chaos synchronization scheme.

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.

scholarly journals Nonlinear control of chaotic systems:A switching manifold approach

2000 ◽  
Vol 4 (4) ◽  
pp. 257-267 ◽  
Author(s):  
Jin-Qing Fang ◽  
Yiguang Hong ◽  
Huashu Qin ◽  
Guanrong Chen
Keyword(s):  
Nonlinear Control ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Control Method ◽  
Initial Conditions ◽  
Design Strategy ◽  
Control Law ◽  
The Lorenz System ◽  
Bang Bang Control ◽  
Nonlinear Control Law

In this paper, a switching manifold approach is developed for nonlinear feed-back control of chaotic systems. The design strategy is straightforward, and the nonlinear control law is the simple bang–bang control. Yet, this control method is very effective; for instance, several desired equilibria can be stabilized by using one control law with different initial conditions. Its effectiveness is verified by both theoretical analysis and numerical simulations. The Lorenz system simulation is shown for the purpose of illustration.

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.

scholarly journals Numerical detection of unstable periodic orbits in continuous-time dynamical systems with chaotic behaviors

2007 ◽  
Vol 14 (5) ◽  
pp. 615-620 ◽  
Author(s):  
Y. Saiki
Keyword(s):  
Dynamical Systems ◽  
Periodic Orbits ◽  
Infinite Number ◽  
Continuous Time ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Complex Phenomenon ◽  
Unstable Periodic Orbits ◽  
Newton Raphson ◽  
The Lorenz System

Abstract. An infinite number of unstable periodic orbits (UPOs) are embedded in a chaotic system which models some complex phenomenon. Several algorithms which extract UPOs numerically from continuous-time chaotic systems have been proposed. In this article the damped Newton-Raphson-Mees algorithm is reviewed, and some important techniques and remarks concerning the practical numerical computations are exemplified by employing the Lorenz system.

scholarly journals Adaptive Projective Synchronization between Two Different Fractional-Order Chaotic Systems with Fully Unknown Parameters

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Liping Chen ◽  
Shanbi Wei ◽  
Yi Chai ◽  
Ranchao Wu
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Projective Synchronization ◽  
Control Law ◽  
Unknown Parameters ◽  
Chen System ◽  
Fractional Order Differential Equations ◽  
Response Systems ◽  
The Stability ◽  
Adaptive Control Law

Projective synchronization between two different fractional-order chaotic systems with fully unknown parameters for drive and response systems is investigated. On the basis of the stability theory of fractional-order differential equations, a suitable and effective adaptive control law and a parameter update rule for unknown parameters are designed, such that projective synchronization between the fractional-order chaotic Chen system and the fractional-order chaotic Lü system with unknown parameters is achieved. Theoretical analysis and numerical simulations are presented to demonstrate the validity and feasibility of the proposed method.

scholarly journals Statistical Modeling in Nonlinear Systems

2005 ◽  
Vol 18 (16) ◽  
pp. 3388-3399 ◽  
Author(s):  
Edward P. Campbell
Keyword(s):  
Nonlinear Dynamics ◽  
Statistical Models ◽  
Lorenz System ◽  
Prediction Models ◽  
Climate Data ◽  
Bayesian Hierarchical ◽  
Alternative Approaches ◽  
The Lorenz System ◽  
Bayesian Hierarchical Methods ◽  
The Impact

Abstract The use of linear statistical methods in building climate prediction models is examined, particularly the use of anomalies. The author’s perspective is that the climate system is a nonlinear interacting system, so the impact of modeling using anomalies rather than observed data directly is considered. With reference to the Lorenz system and a simple model for regime dependence, it is shown that anomalies impair our ability to reconstruct nonlinear dynamics. Some alternative approaches in the literature that offer an attractive way forward are explored, focusing on Bayesian hierarchical methods to construct so-called physical–statistical models. The author’s view is that anomalies should be reserved in most cases as a tool for enhancing graphical representations of climate data. The exceptions are when the implicit assumptions underlying the use of anomalies are met or when an anomaly representation is physically motivated.

PARTIAL STATE IMPULSIVE SYNCHRONIZATION OF A CLASS OF NONLINEAR SYSTEMS

2009 ◽  
Vol 19 (01) ◽  
pp. 387-393 ◽  
Author(s):  
YAN-WU WANG ◽  
CHANGYUN WEN ◽  
YENG CHAI SOH ◽  
ZHI-HONG GUAN
Keyword(s):  
Nonlinear System ◽  
Theoretical Analysis ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Hyperchaotic System ◽  
Impulsive Synchronization ◽  
Partial State ◽  
Simulation Results ◽  
System States ◽  
Synchronization Scheme

Impulsive synchronization of chaotic systems is an attractive topic and a number of interesting results have been obtained in recent years. However, all of these results on impulsive synchronization need to employ full states of the system to achieve the desired objectives. In this paper, impulsive synchronization that needs only part of system states is studied for a class of nonlinear system. Typical chaotic systems, such as Lorenz system, Chen's system, and a 4D hyperchaotic system, are taken as examples. A new scheme is proposed to select the impulsive intervals. After some theoretical analysis, simulation results show the effectiveness of the proposed synchronization scheme.

GENERALIZED SYNCHRONIZATION OF NONIDENTICAL FRACTIONAL-ORDER CHAOTIC SYSTEMS

2013 ◽  
Vol 27 (30) ◽  
pp. 1350195 ◽  
Author(s):  
XING-YUAN WANG ◽  
ZUN-WEN HU ◽  
CHAO LUO
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Pole Placement ◽  
Generalized Synchronization ◽  
Chen System ◽  
Hyperchaotic Lorenz System ◽  
The Stability ◽  
Synchronization Scheme ◽  
Placement Technique

In this paper, a chaotic synchronization scheme is proposed to achieve the generalized synchronization between two different fractional-order chaotic systems. Based on the stability theory of fractional-order systems and the pole placement technique, a controller is designed and theoretical proof is given. Two groups of examples are shown to verify the effectiveness of the proposed scheme, the first one is to realize the generalized synchronization between the fractional-order Chen system and the fractional-order Rössler system, the second one is between the fractional-order Lü system and the fractional-order hyperchaotic Lorenz system. The corresponding numerical simulations verify the effectiveness of the proposed scheme.

Sign in / Sign up

Export Citation Format

Share Document