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.

A COMMON PHENOMENON IN CHAOTIC SYSTEMS LINKED BY TIME DELAY

2006 ◽  
Vol 16 (12) ◽  
pp. 3727-3736 ◽  
Author(s):  
PEI YU ◽  
FEI XU
Keyword(s):  
Time Delay ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Common Phenomenon ◽  
State Variables ◽  
Chen System ◽  
The Family ◽  
The Lorenz System ◽  
Parameter Values ◽  
Liu System

In this paper, we report a common phenomenon observed in chaotic systems linked by time delay. Recently, the Lorenz chaotic system has been extended to the family of Lorenz systems which includes the Chen and Lü systems. These three chaotic systems, corresponding to different sets of system parameter values, are topologically different. With the aid of numerical simulations, we have surprisingly found that a simple time delay, directly applied to one or more state variables, transforms the Lorenz system to the generalized Chen system or the generalized Lü system without any parameter changes. The existence of this phenomenon has also been found in other known chaotic systems: the Rössler system, the Chua's circuit and the 4-Liu system. This finding has shown a common characteristic of chaotic systems: a new chaotic "branch" can be created from a chaotic attractor by simply adding a time delay.

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.

Adaptive Switching Control for Projected Synchronization of Chaotic Systems with Uncertainties

2012 ◽  
Vol 499 ◽  
pp. 360-365
Author(s):  
Li Ming Du ◽  
Feng Ying Wang ◽  
Jin Xiang Pian ◽  
Zi Yang Han
Keyword(s):  
Lyapunov Function ◽  
Function Method ◽  
Chaotic Systems ◽  
Switching Control ◽  
Projective Synchronization ◽  
Synchronization Problem ◽  
Control Scheme ◽  
Lyapunov Function Method ◽  
Adaptive Switching Control ◽  
Liu System

This paper is concerned with the projective synchronization problem for a class of chaotic system with uncertainties. By utilizing single Lyapunov function method, an adaptive switching control scheme for the synchronization has been presented. Simulation examples, the chaotic Liu system are given to show the feasibility and effectiveness of the proposed theory and method.

Adaptive Synchronization of Time-Delay Chaotic Systems with Intermittent Control

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Yuangan Wang ◽  
Dong Li
Keyword(s):  
Time Delay ◽  
Nonlinear Systems ◽  
Lyapunov Stability ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Adaptive Synchronization ◽  
Intermittent Control ◽  
Periodically Intermittent Control ◽  
Control Scheme ◽  
The Lorenz System

AbstractTime delay is a common but not negligible phenomenon in nonlinear systems, which affects the performance of synchronization. Based on principles of intermittent control and Lyapunov stability theories, we establish the synchronization criteria of the time-delay chaotic systems via adaptive intermittent control. The proposed control scheme is under aperiodically intermittent control, which is also extended to periodically intermittent control to better realization. Finally, to verify the effectiveness of our results, we choose the Lorenz system to do simulation.

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.

PROJECTIVE SYNCHRONIZATION OF UNIDENTICAL CHAOTIC SYSTEMS BASED ON STABILITY CRITERION

2006 ◽  
Vol 16 (04) ◽  
pp. 1049-1056 ◽  
Author(s):  
HONGJIE YU ◽  
JIANHUA PENG ◽  
YANZHU LIU
Keyword(s):  
Linear Systems ◽  
Stability Criterion ◽  
Chaotic Systems ◽  
Three Dimensional ◽  
New Method ◽  
Projective Synchronization ◽  
Partially Linear ◽  
Higher Dimensional ◽  
The Lorenz System ◽  
The Stability

A new method of projective synchronization of unidentical chaotic systems is proposed in this letter. This method is based on the stability criterion of linear systems. The response of two unidentical chaotic systems can synchronize up to any desired scaling factor by a suitable separation of the systems. The new method of projective synchronization is suitable not only for the three-dimensional coupled partially linear systems, but also for higher dimensional even hyperchaotic systems. The simplicity and effectiveness of the proposed method are illustrated by the Lorenz system, the four-dimensional partially linear system, the four-dimensional hyperchaotic Rösser system and Chua's circuit system as four numerical examples.

COMPOSITE SLIDING MODE CONTROL OF CHAOTIC SYSTEMS WITH UNCERTAINTIES

2003 ◽  
Vol 13 (04) ◽  
pp. 863-878 ◽  
Author(s):  
CHUN-CHIEH WANG ◽  
JUHNG-PERNG SU
Keyword(s):  
Sliding Mode Control ◽  
High Performance ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Sliding Mode ◽  
Dynamic Responses ◽  
Significant Feature ◽  
New Approach ◽  
Mode Control ◽  
Control Scheme

This paper presents a new approach to the design of a composite sliding mode control for a class of chaotic systems with uncertainties. A significant feature of this control scheme is the incorporation of a new complementary sliding variable to the conventional sliding variable in order that a high-performance controller can be obtained. It has been shown that the guaranteed steady-state error bounds are reduced by half, as compared with the conventional sliding control. Moreover, the dynamic responses during the reaching phase are also significantly improved. We used a controlled uncertain Lorenz system and a controlled uncertain Chua's circuit as illustrative examples to demonstrate the effectiveness of the design.

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