New complex projective synchronization strategies for drive-response networks with fractional complex-variable dynamics

Xu, Quan; Xu, Xiaolong; Zhuang, Shengxian; Xiao, Jixue; Chen, Song; Che, Chang

doi:10.1016/j.amc.2018.06.055

Cited by 22 publications

(15 citation statements)

References 35 publications

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“…Given that

results in:

Since

is Hermitian Matrix:

where

and

are the minimum and maximum eigenvalue of

, respectively [ 36 , 37 ].…”

Section: Resultsmentioning

confidence: 99%

Adaptive Synchronization of Fractional-Order Complex Chaotic system with Unknown Complex Parameters

Zhang

Liu

Yang

2019

Entropy

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This paper investigates the problem of synchronization of fractional-order complex-variable chaotic systems (FOCCS) with unknown complex parameters. Based on the complex-variable inequality and stability theory for fractional-order complex-valued system, a new scheme is presented for adaptive synchronization of FOCCS with unknown complex parameters. The proposed scheme not only provides a new method to analyze fractional-order complex-valued system but also significantly reduces the complexity of computation and analysis. Theoretical proof and simulation results substantiate the effectiveness of the presented synchronization scheme.

show abstract

“…Given that

results in:

Since

is Hermitian Matrix:

where

and

are the minimum and maximum eigenvalue of

, respectively [ 36 , 37 ].…”

Section: Resultsmentioning

confidence: 99%

Adaptive Synchronization of Fractional-Order Complex Chaotic system with Unknown Complex Parameters

Zhang

Liu

Yang

2019

Entropy

View full text Add to dashboard Cite

show abstract

“…Two numerical examples are given at last to show the correctness and feasibility of the proposed results. Based on the study method presented in this paper and the idea of driving-response conception [35,41], we will attempt to study the synchronization problem for a class of chaotic complex-valued neural networks with mixed delays and stochastic disturbances in the near future. Besides, numerous references concerning neural networks with impulsive effect have been emerged in the past two decades; see [5, 9-15, 22, 40, 42].…”

Section: Discussionmentioning

confidence: 99%

Mean Square Exponential Stability of Stochastic Complex‐Valued Neural Networks with Mixed Delays

Yang

2019

Complexity

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This paper investigates the mean square exponential stability problem of a class of complex-valued neural networks with stochastic disturbance and mixed delays including both time-varying delays and continuously distributed delays. Under different assumption conditions concerning stochastic disturbance term from the existing ones, some sufficient conditions are derived for assuring the mean square exponential stability of the equilibrium point of the system based on the vector Lyapunov function method and Ito^ differential-integral theorem. The obtained results not only generalize the existing ones, but also reduce the conservatism of the previous stability results about complex-valued neural networks with stochastic disturbances. Two numerical examples with simulation results are given to verify the feasibility of the proposed results.

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“…In addition to impulse disturbances [13-15, 34, 35] and parameter uncertainties [2,31,34], stochastic disturbances [10,38] also exist in real complex-valued neural networks. Additionally, the stability problem and the synchronization problem of fractional-order systems have become a hot research topic [39,40]. The research in this paper can be extended further to the study of the stability of the mentioned systems.…”

Section: Complexitymentioning

confidence: 93%

Robust Exponential Stability of Switched Complex‐Valued Neural Networks with Interval Parameter Uncertainties and Impulses

Xue

Peng

et al. 2018

Complexity

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In this paper, dynamic behavior analysis has been discussed for a class of switched complex-valued neural networks with interval parameter uncertainties and impulse disturbance. Sufficient conditions for guaranteeing the existence, uniqueness, and global robust exponential stability of the equilibrium point have been obtained by using the homomorphism mapping theorem, the scalar Lyapunov function method, the average dwell time method, and M-matrix theory. Since there is no result concerning the stability problem of switched neural networks defined in complex number domain, the stability results we describe in this paper generalize the existing ones. The effectiveness of the proposed results is illustrated by a numerical example.

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New complex projective synchronization strategies for drive-response networks with fractional complex-variable dynamics

Cited by 22 publications

References 35 publications

Adaptive Synchronization of Fractional-Order Complex Chaotic system with Unknown Complex Parameters

Adaptive Synchronization of Fractional-Order Complex Chaotic system with Unknown Complex Parameters

Mean Square Exponential Stability of Stochastic Complex‐Valued Neural Networks with Mixed Delays

Robust Exponential Stability of Switched Complex‐Valued Neural Networks with Interval Parameter Uncertainties and Impulses

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