Optimal phase synchronization in networks of phase-coherent chaotic oscillators

Skardal, Per Sebastian; Sevilla-Escoboza, R.; Vera-Ávila, V. P.; Buldú, Javier M.

doi:10.1063/1.4974029

Cited by 21 publications

(16 citation statements)

References 36 publications

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“…Previous analyses of synchronization of nonidentical chaotic oscillators have focused mainly on cluster synchronization [7,8] and phase synchronization [9][10][11][12][13]. For example, oscillator heterogeneity has been shown to mediate relay synchronization [14][15][16] and to induce frequency locking by suppressing chaos [17][18][19][20].…”

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confidence: 99%

Synchronizing Chaos with Imperfections

2021

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Previous research on nonlinear oscillator networks has shown that chaos synchronization is attainable for identical oscillators but deteriorates in the presence of parameter mismatches. Here, we identify regimes for which the opposite occurs and show that oscillator heterogeneity can synchronize chaos for conditions under which identical oscillators cannot. This effect is not limited to small mismatches and is observed for random oscillator heterogeneity on both homogeneous and heterogeneous network structures. The results are demonstrated experimentally using networks of Chua's oscillators and are further supported by numerical simulations and theoretical analysis. In particular, we propose a general mechanism based on heterogeneity-induced mode mixing that provides insights into the observed phenomenon. Since individual differences are ubiquitous and often unavoidable in real systems, it follows that such imperfections can be an unexpected source of synchronization stability.

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confidence: 99%

Synchronizing Chaos with Imperfections

2021

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“…Synchronization is achieved for the drive-response neural network system when the derived error system states become stable over time. Complete synchronization [15], generalized synchronization [16], quasi-synchronization [17], anti-synchronization, projective synchronization [18], exponential synchronization [19], cluster synchronization [20] and phase synchronization [21] are now just a few examples of synchronization schemes suggested both theoretically and practically. Among all types of chaotic synchronizations, projective synchronization represents that under a suitable controller, the slave neural network is synchronized to the master neural network by a proportional factor, demonstrates that different types of synchronization can be obtained by selecting different projection coefficients.…”

Section: Introductionmentioning

confidence: 99%

Synchronization of time-varying time delayed neutral-type neural networks for finite-time in complex field

Jayanthi¹,

Santhakumari²

2021

Math. Model. Comput.

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This paper deals with the problem of finite-time projective synchronization for a class of neutral-type complex-valued neural networks (CVNNs) with time-varying delays. A simple state feedback control protocol is developed such that slave CVNNs can be projective synchronized with the master system in finite time. By employing inequalities technique and designing new Lyapunov--Krasovskii functionals, various novel and easily verifiable conditions are obtained to ensure the finite-time projective synchronization. It is found that the settling time can be explicitly calculated for the neutral-type CVNNs. Finally, two numerical simulation results are demonstrated to validate the theoretical results of this paper.

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“…Its generic formulation allowed researchers to use it to model several applications, ranging from biology, e.g., neurons firing in synchrony, to engineering, e.g., power grids [4]. The ubiquity of synchronization in many natural or artificial systems has naturally raised questions about the stability and robustness of synchronized states [5][6][7][8]. In their seminal work, Pecora & Caroll [9] introduced a method known as Master Stability Function (MSF) to help understand the role that the topology of interactions has on system stability.…”

Section: Introductionmentioning

confidence: 99%

Synchronization dynamics in non-normal networks: the trade-off for optimality

Muolo,

Carletti,

Gleeson

et al. 2020

Preprint

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Synchronization is an important behavior that characterizes many natural and human made systems composed by several interacting units. It can be found in a broad spectrum of applications, ranging from neuroscience to power-grids, to mention a few. Such systems synchronize because of the complex set of coupling they exhibit, the latter being modeled by complex networks. The dynamical behavior of the system and the topology of the underlying network are strongly intertwined, raising the question of the optimal architecture that makes synchronization robust. The Master Stability Function (MSF) has been proposed and extensively studied as a generic framework to tackle synchronization problems. Using this method, it has been shown that for a class of models, synchronization in strongly directed networks is robust to external perturbations. In this paper, our approach is to transform the non-autonomous system of coupled oscillators into an autonomous one, showing that previous results are model-independent. Recent findings indicate that many real-world networks are strongly directed, being potential candidates for optimal synchronization. Inspired by the fact that highly directed networks are also strongly non-normal, in this work, we address the matter of non-normality by pointing out that standard techniques, such as the MSF, may fail in predicting the stability of synchronized behavior. These results lead to a trade-off between nonnormality and directedness that should be properly considered when designing an optimal network, enhancing the robustness of synchronization.

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Optimal phase synchronization in networks of phase-coherent chaotic oscillators

Cited by 21 publications

References 36 publications

Synchronizing Chaos with Imperfections

Synchronizing Chaos with Imperfections

Synchronization of time-varying time delayed neutral-type neural networks for finite-time in complex field

Synchronization dynamics in non-normal networks: the trade-off for optimality

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