Complete synchronization of two Chen-Lee systems

Sheu

et al. 2011

Int. J. Mod. Phys. B

The impulsive synchronization of two chaotic Chen-Lee systems was investigated in this paper. Based on Lyapunov's direct method, sufficient conditions for the global exponential synchronization and global asymptotical synchronization were derived. Further, the theoretical results were verified by a numerical simulation. In addition, the impulsive synchronization of two chaotic Chen-Lee systems was also implemented using an electronic circuit.

Section: An Illustrative Examplementioning

confidence: 99%

“…It was proven that this system is the governing set of equations for gyro motion with feedback control. Complete synchronization, controlling chaos with multiple time-delays, electronic circuit implementation, fractional-order behavior, and other aspects of this system [18][19][20][21][22][23][24] have recently been studied.…”

Section: Introductionmentioning

confidence: 99%

Impulsive Synchronization and Its Implementation in Chen–lee Systems

Sheu

et al. 2011

Int. J. Mod. Phys. B

“…The system is then called the Chen-Lee system [19]. Complete synchronization [20], synchronization and antisynchronization [21], controlling chaos with multiple time-delays [22], electronic circuit implementation [23,24], fractional-order behavior [19,25], and so forth have been studied for this system recently. It is believed that hyperchaotic systems are demanded by practical engineering applications, such as secure communication.…”

Section: Introductionmentioning

confidence: 99%

Hybrid Stability Checking Method for Synchronization of Chaotic Fractional-Order Systems

Abstract and Applied Analysis

Chen

et al. 2014

A hybrid stability checking method is proposed to verify the establishment of synchronization between two hyperchaotic systems. During the design stage of a synchronization scheme for chaotic fractional-order systems, a problem is sometimes encountered. In order to ensure the stability of the error signal between two fractional-order systems, the arguments of all eigenvalues of the Jacobian matrix of the erroneous system should be within a region defined in Matignon’s theorem. Sometimes, the arguments depend on the state variables of the driving system, which makes it difficult to prove the stability. We propose a new and efficient hybrid method to verify the stability in this situation. The passivity-based control scheme for synchronization of two hyperchaotic fractional-order Chen-Lee systems is provided as an example. Theoretical analysis of the proposed method is validated by numerical simulation in time domain and examined in frequency domain via electronic circuits.

“…The system is then called the Chen-Lee system [15]. Complete synchronization [16], synchronization and anti-synchronization [17], controlling chaos with multiple time-delays [18], electronic circuit implementation [19], fractional-order behavior [15], synchronization with commensurate and incommensurate fractional orders [20], etc. have been studied for this system recently.…”

Section: Introductionmentioning

confidence: 99%

Hybrid Projective Synchronization for the Fractional-Order Chen-Lee System and its Circuit Realization

Chen

et al. 2013

AMM

The growing interest shows the importance of the control of chaos in fractional-order systems in recent years. This paper investigates in the hybrid projective synchronization of two chaotic systems with fractional-order, which were derived from Euler equations of rigid body motion. Theoretical analyses of the proposed methods are validated by numerical simulation in the time domain. Moreover, the synchronization system is realized using electronic circuits with fractance in the frequency domain.