Adaptive coupling and enhanced synchronization in coupled phase oscillators

Ren, Quansheng; Zhao, Jianye

doi:10.1103/physreve.76.016207

Cited by 93 publications

(84 citation statements)

References 26 publications

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“…15 (c) via varying the value of λ and fixing T = 15, showing the striking result that the adaptive mechanism generally enhances global synchronization r(t) for t > 0 in comparison to that for t < 0. This result was also observed with different adaptive mechanisms [224]. Figure 15 plots the global synchronization r in (a) and the local synchornization r link (b) with respect to λ and T .…”

Section: Time-varying Couplingsupporting

confidence: 65%

The Kuramoto model in complex networks

et al. 2016

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Synchronization of an ensemble of oscillators is an emergent phenomenon present in several complex systems, ranging from social and physical to biological and technological systems. The most successful approach to describe how coherent behavior emerges in these complex systems is given by the paradigmatic Kuramoto model. This model has been traditionally studied in complete graphs. However, besides being intrinsically dynamical, complex systems present very heterogeneous structure, which can be represented as complex networks. This report is dedicated to review main contributions in the field of synchronization in networks of Kuramoto oscillators. In particular, we provide an overview of the impact of network patterns on the local and global dynamics of coupled phase oscillators. We cover many relevant topics, which encompass a description of the most used analytical approaches and the analysis of several numerical results. Furthermore, we discuss recent developments on variations of the Kuramoto model in networks, including the presence of noise and inertia. The rich potential for applications is discussed for special fields in engineering, neuroscience, physics and Earth science. Finally, we conclude by discussing problems that remain open after the last decade of intensive research on the Kuramoto model and point out some promising directions for future research.

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Section: Time-varying Couplingsupporting

confidence: 65%

The Kuramoto model in complex networks

et al. 2016

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“…The idea of plastic synapses improving synchronization has been taken up in several subsequent works including a study on enhancement of synchronization in neuronal ensembles 63,64 and the interaction of two neurons with less regular intrinsic activity. 65 It was also used in more applied work; e.g., for how to avoid pathological synchronization states that may have come about by the STDP of excitatory connectivity with deep brain stimulation.…”

Section: B Synchronization With Stdp Synapsesmentioning

confidence: 99%

Neuronal synchrony: Peculiarity and generality

Nowotny

Huerta²,

Rabinovich³

2008

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Synchronization in neuronal systems is a new and intriguing application of dynamical systems theory. Why are neuronal systems different as a subject for synchronization? ͑1͒ Neurons in themselves are multidimensional nonlinear systems that are able to exhibit a wide variety of different activity patterns. Their "dynamical repertoire" includes regular or chaotic spiking, regular or chaotic bursting, multistability, and complex transient regimes. ͑2͒ Usually, neuronal oscillations are the result of the cooperative activity of many synaptically connected neurons ͑a neuronal circuit͒. Thus, it is necessary to consider synchronization between different neuronal circuits as well. ͑3͒ The synapses that implement the coupling between neurons are also dynamical elements and their intrinsic dynamics influences the process of synchronization or entrainment significantly. In this review we will focus on four new problems: ͑i͒ the synchronization in minimal neuronal networks with plastic synapses ͑synchronization with activity dependent coupling͒, ͑ii͒ synchronization of bursts that are generated by a group of nonsymmetrically coupled inhibitory neurons ͑heteroclinic synchronization͒, ͑iii͒ the coordination of activities of two coupled neuronal networks ͑partial synchronization of small composite structures͒, and ͑iv͒ coarse grained synchronization in larger systems ͑synchronization on a mesoscopic scale͒. © 2008 American Institute of Physics. ͓DOI: 10.1063/1.2949925͔The observation of synchrony (coherence, correlation) in the brain and the entire nervous system has a long history. Neuronal synchronization has been experimentally analyzed on many different levels of system complexity. Even though the functional role of this phenomenon is still not absolutely clear, neuroscientists agree that the level of synchrony is one of the key characteristics of the activity of the brain/neuronal systems in general. Both limit cases, too strong and too weak synchronization are characteristic for certain brain disorders, such as epilepsy, Parkinson's disease, Alzheimer's disease, and schizophrenia (see Refs. 1 and 2). In this short review we discuss a few mechanisms of neuronal synchronization that illustrate the specificity of the corresponding phenomena in neuronal circuits, and their similarity to classical examples in physical systems. We also discuss briefly the influence of the complexity of real neuronal systems on synchronous dynamics.

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“…(7) is a saturating term which prevents coupling coefficients from increasing or decreasing without bound. A hard bound such as restricting |K ij | ≤ 1 as in [25] can effectively limit the steady state values of the coupling coefficients to one of the two hard bounds. Although such restrictions can account for the memorization of binary data, a soft bound such as the saturating term we enlist here can allow the network to possess more diverse connectivity.…”

Section: The Modelmentioning

confidence: 99%

“…Recent theoretical efforts have studied how a network may develop in accordance with neural learning mechanisms in relation to the dynamics of synchronous cluster formation [21,24,25,26,27]. Neurophysiological studies have shown that a synapse is strengthened if the pre-synaptic neuron repeatedly causes the post-synaptic neuron to fire, leading to the Long Term Potentiation (LTP) of the synapse [28,29].…”

Section: Introductionmentioning

confidence: 99%

Learning-rate-dependent clustering and self-development in a network of coupled phase oscillators

Niyogi

English

2009

Phys. Rev. E

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We investigate the role of the learning rate in a Kuramoto Model of coupled phase oscillators in which the coupling coefficients dynamically vary according to a Hebbian learning rule. According to the Hebbian theory, a synapse between two neurons is strengthened if they are simultaneously co-active. Two stable synchronized clusters in anti-phase emerge when the learning rate is larger than a critical value. In such a fast learning scenario, the network eventually constructs itself into an all-to-all coupled structure, regardless of initial conditions in connectivity. In contrast, when learning is slower than this critical value, only a single synchronized cluster can develop. Extending our analysis, we explore whether self-development of neuronal networks can be achieved through an interaction between spontaneous neural synchronization and Hebbian learning. We find that selfdevelopment of such neural systems is impossible if learning is too slow. Finally, we demonstrate that similar to the acquisition and consolidation of long-term memory, this network is capable of generating and remembering stable patterns.

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Adaptive coupling and enhanced synchronization in coupled phase oscillators

Cited by 93 publications

References 26 publications

The Kuramoto model in complex networks

The Kuramoto model in complex networks

Neuronal synchrony: Peculiarity and generality

Learning-rate-dependent clustering and self-development in a network of coupled phase oscillators

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