Inverse chaos synchronization in linearly and nonlinearly coupled systems with multiple time-delays

Shahverdiev, E.M.; Hashimov, R.H.; Nuriev, R. A.; Hashimova, L.H.; Huseynova, E.M.; Shore, K.A.

doi:10.1016/j.chaos.2005.08.059

Cited by 14 publications

(10 citation statements)

References 35 publications

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“…In anticipating synchronisation [16][17] the driven system state is synchronised to the future state of the driver system. For some other types of synchronisation see other references [18][19][20][21] also.…”

Section: Introductionmentioning

confidence: 99%

Modulated Feedback and Coupling Time Delays, and All-to-all Chaos Synchronisation in a Network of Networks: One of the Simplest Cases

Shahverdiev

Bayramov

Nuriev

et al. 2018

AJR2P

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The study reports on all- to- all chaos synchronisation in a network of networks based on the Ikeda model. The study considered one of the simplest cases. It found the existence and stability conditions for such a synchronisation regime. Numerical simulations validated the analytical findings. The results can be of certain importance in achieving high- level output for the coupled systems and information processing.

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Section: Introductionmentioning

confidence: 99%

Modulated Feedback and Coupling Time Delays, and All-to-all Chaos Synchronisation in a Network of Networks: One of the Simplest Cases

Shahverdiev

Bayramov

Nuriev

et al. 2018

AJR2P

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“…To appreciate the chaotic and hyperchaotic nature of the uncoupled system, we present in Fig. 8a the first eleven largest Lyapunov exponents for the above values of the parameters in the range of delay time τ ∈ (2,25) where several of them take positive values. As an illustration, the hyperchaotic attractor with three positive Lyapunov exponents of the uncoupled system for τ 1 = τ = 4.0 is depicted in Fig.…”

Section: A Inverse Anticipatory Synchronization Iasmentioning

confidence: 99%

“…Experimental observations and numerical simulations of synchronization and inverse synchronization of low frequency power drop-outs and jump-ups of chaotic semiconductor lasers were carried out in [23]. Inverse synchronization was also observed both experimentally and numerically in unidirectionally coupled laser systems with optical feedback [24,27], as well as in a class of chaotic delayed neural networks [28] and in coupled Ikeda systems with multi-feedback and multiple time-delays [25]. Inverse anticipating synchronization was demonstrated in coupled Ikeda systems [22].…”

Section: Introductionmentioning

confidence: 98%

Inverse synchronizations in coupled time-delay systems with inhibitory coupling

Senthilkumar

Kurths

Lakshmanan

2009

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Transitions between inverse anticipatory, inverse complete, and inverse lag synchronizations are shown to occur as a function of the coupling delay in unidirectionally coupled time-delay systems with inhibitory coupling. We have also shown that the same general asymptotic stability condition obtained using the Krasovskii-Lyapunov functional theory can be valid for the cases where (i) both the coefficients of the Delta(t) (error variable) and Delta(tau)=Delta(t-tau) (error variable with delay) terms in the error equation corresponding to the synchronization manifold are time independent and (ii) the coefficient of the Delta term is time independent, while that of the Delta(tau) term is time dependent. The existence of different kinds of synchronization is corroborated using similarity function, probability of synchronization, and also from changes in the spectrum of Lyapunov exponents of the coupled time-delay systems.

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“…In the same year, Sun (2004) studied the chaos synchronization of time-delay system using the unidirectional linear error feedback coupling with time-delay. In 2013, Shahverdiev et al (2013) made the first report on inverse chaos synchronization between bidirectionally nonlinearly and linearly coupled variable multiple time delay laser systems governed by the Ikeda model (Shahverdiev et al, 2006). In 2016, Kazemy and Farrokhi (2016) proposed a delay-dependent synchronization criterion in the form of linear matrix inequalities (LMIs) for a chaotic Lur’e system.…”

Section: Introductionmentioning

confidence: 99%

Robust finite-time chaos synchronization of time-delay chaotic systems and its application in secure communication

Wang

Miao

et al. 2016

Transactions of the Institute of Measurement and Control

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This paper presents finite-time chaos synchronization of time-delay chaotic systems with uncertain parameters. According to the proposed method, a lot of coupled items can be treated as zero items. Thus, the whole system can be simplified greatly. Based on robust chaotic synchronization, secure communication can be realized with a wide range of parameter disturbance and time-delay. Numerical simulations are provided to illustrate the effectiveness of the proposed method.

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Inverse chaos synchronization in linearly and nonlinearly coupled systems with multiple time-delays

Cited by 14 publications

References 35 publications

Modulated Feedback and Coupling Time Delays, and All-to-all Chaos Synchronisation in a Network of Networks: One of the Simplest Cases

Modulated Feedback and Coupling Time Delays, and All-to-all Chaos Synchronisation in a Network of Networks: One of the Simplest Cases

Inverse synchronizations in coupled time-delay systems with inhibitory coupling

Robust finite-time chaos synchronization of time-delay chaotic systems and its application in secure communication

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