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 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 Chaotic Systems with Time Delays via Periodically Intermittent Control

2017 ◽  
Vol 26 (09) ◽  
pp. 1750139 ◽  
Author(s):  
Chao Liu ◽  
Zheng Yang ◽  
Dihua Sun ◽  
Xiaoyang Liu ◽  
Wanping Liu
Keyword(s):  
Time Delay ◽  
Time Delays ◽  
Chaotic Systems ◽  
Control Period ◽  
Feasible Region ◽  
Intermittent Control ◽  
Periodically Intermittent Control ◽  
First Order ◽  
Response System ◽  
System With Time Delay

This paper investigates the exponential synchronization of chaotic systems with time delays via periodically intermittent control. Under the new differential inequality, some novel synchronization criteria are derived. In contrast to the existing works, the proposed results are less conservative because they can obtain more precise synchronized rate under the identical control conditions and remove the restrictions on the control period (or the control width) and the time delay. By using special parameters, the feasible region D(ξ), which guarantees the response system synchronizes with the drive system with synchronized rate 0.5ξ, is obtained. The Lu chaotic attractor and a first-order chaotic system with time delay are presented to demonstrate the effectiveness of the proposed results.

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 Control Scheme for a Fractional-Order Chaotic Genesio-Tesi Model

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
Changjin Xu ◽  
Peiluan Li ◽  
Maoxin Liao ◽  
Zixin Liu ◽  
Qimei Xiao ◽  
...  
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Fractional Order ◽  
Characteristic Equation ◽  
Chaotic Systems ◽  
Chaotic Behavior ◽  
Feedback Controllers ◽  
Control Scheme ◽  
The Stability ◽  
Time Delayed Feedback

In this paper, based on the earlier research, a new fractional-order chaotic Genesio-Tesi model is established. The chaotic phenomenon of the fractional-order chaotic Genesio-Tesi model is controlled by designing two suitable time-delayed feedback controllers. With the aid of Laplace transform, we obtain the characteristic equation of the controlled chaotic Genesio-Tesi model. Then by regarding the time delay as the bifurcation parameter and analyzing the characteristic equation, some new sufficient criteria to guarantee the stability and the existence of Hopf bifurcation for the controlled fractional-order chaotic Genesio-Tesi model are derived. The research shows that when time delay remains in some interval, the equilibrium point of the controlled chaotic Genesio-Tesi model is stable and a Hopf bifurcation will happen when the time delay crosses a critical value. The effect of the time delay on the stability and the existence of Hopf bifurcation for the controlled fractional-order chaotic Genesio-Tesi model is shown. At last, computer simulations check the rationalization of the obtained theoretical prediction. The derived key results in this paper play an important role in controlling the chaotic behavior of many other differential chaotic systems.

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