Binary generalized synchronization

Короновский, А. А.; Москаленко, О. И.; Ponomarenko, V. I.; Прохоров, М. Д.; Hramov, Alexander E.

doi:10.1016/j.chaos.2015.11.045

Cited by 10 publications

(6 citation statements)

References 67 publications

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“…The synchronization order parameter (7) cannot describe the strong correlations and dimensional reduction that occur before synchronization. For the simple model (2) used to illustrate this phenomenon, characterization of the correlations might be obtained by the projections on the eigenvectors of the Lyapunov matrix, which are exactly known in this case.…”

Section: The Models 21 a Deformed Kuramoto Modelmentioning

confidence: 99%

“…Synchronization in complex systems [1] [2] [3] [4] [5] [6] [7] is a striking cooperative phenomena in Nature that has been shown to be of fundamental importance in fields as diverse as the operation of heart pacemaker cells [8] [9], circadian cycles [10], epileptic seizures [11] [12], schizophrenia disorders [13] [14], neuronal firing [15] [16] [17], animal behavior [18], social fads, the integration of cognitive tasks [19] [20] [21], synchronization-based computation [22] and even quantum systems [23].…”

Section: Introductionmentioning

confidence: 99%

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Characterizing correlations and synchronization in collective dynamics

Aguirre,

Mendes

2017

Preprint

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Synchronization, that occurs both for non-chaotic and chaotic systems, is a striking phenomenon with many practical implications in natural phenomena. However, even before synchronization, strong correlations occur in the collective dynamics of complex systems. To characterize their nature is essential for the understanding of phenomena in physical and social sciences. The emergence of strong correlations before synchronization is illustrated in a few piecewise linear models. They are shown to be associated to the behavior of ergodic parameters which may be exactly computed in some models. The models are also used as a testing ground to find general methods to characterize and parametrize the correlated nature of collective dynamics.

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Section: The Models 21 a Deformed Kuramoto Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Characterizing correlations and synchronization in collective dynamics

Aguirre,

Mendes

2017

Preprint

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show abstract

“…After decades of the development, the synchronization forms of complex networks have become more diverse. Apart from global synchronization, 8 robust synchronization 9 in the past, some novel synchronization types, such as generalized synchronization, 10 cluster synchronization, 11 and impulsive synchronization 12 have been discussed in depth.…”

Section: Introductionmentioning

confidence: 99%

Impulsive adaptive pinning synchronization of Lur'e networks with cluster‐tree topology via parameters variation protocols

Xuan

Tang

Park

et al. 2021

Adaptive Control & Signal

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This article is devoted to studying the problem of globally and exponentially adaptive cluster synchronization for a class of Lur'e dynamical networks with multiple time-varying delays and hybrid couplings. A novel impulsive adaptive pinning feedback control protocol is proposed with fully considering the cluster-tree topology structures of the networks and only imposed on the Lur'e systems in current cluster which exist directed paths with those Lur'e systems in the other clusters. In view of the concept of average impulsive interval, the comparison principle, the extended parameter variation methods, and the reductio ad absurdum, sufficient conditions are acquired for achieving the cluster synchronization of the derivative coupled Lur'e networks with considering different functions of the impulsive effects, respectively. Furthermore, according to the designed adaptive updating law, suitable feedback control strengths are obtained, which largely save the control costs. Finally, the effectiveness of the control schemes and the theoretical results have been proved by executing two numerical simulation examples.

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“…Since the pioneering work by Pecora and Carroll [1], chaos synchronization, a very active topic in nonlinear science, has received increasing attention. The concept of synchronization has been extended in scope, for example to generalized synchronization [2]- [4], phase synchronization [5], lag synchronization [6], and even anti-phase synchronization (APS) [7]- [9]. APS can also be interpreted as anti-synchronization (AS), which is a phenomenon in which the state variables of the synchronized systems have the same amplitude as but opposite signs to those of the driving system.…”

Section: Introductionmentioning

confidence: 99%

Chaos Anti-Synchronization between Chen System and Genesio System

Wu¹,

Wu²,

Yan³

et al. 2016

OALib

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In this paper, anti-synchronization of two different chaotic systems is investigated. On the basis of Lyapunov theory, adaptive control scheme is proposed when system parameters are unknown or uncertain; sufficient conditions for the stability of the error dynamics are derived, where the controllers are designed by using the sum of the state variables in chaotic systems. Numerical simulations are performed for the Chen system and Genesio system to demonstrate the effectiveness of the proposed control strategy.

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Binary generalized synchronization

Cited by 10 publications

References 67 publications

Characterizing correlations and synchronization in collective dynamics

Characterizing correlations and synchronization in collective dynamics

Impulsive adaptive pinning synchronization of Lur'e networks with cluster‐tree topology via parameters variation protocols

Chaos Anti-Synchronization between Chen System and Genesio System

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