Phase synchronization of coupled bursting neurons and the generalized Kuramoto model

Ferrari, Fernanda; Viana, Ricardo L.; Lopes, S. R.; Stoop, Ruedi

doi:10.1016/j.neunet.2015.03.003

Cited by 60 publications

(26 citation statements)

References 81 publications

(89 reference statements)

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“…Furthermore, several studies have analyzed synchronization phenomena typified by chaos synchronization and phase synchronization among neurons, and with external input signals, in spiking neural networks with chaotic spiking activity 18–21 . Among these synchronization phenomena, it has been known that fluctuating activities in deterministic chaos cause a phenomenon that is similar to SR.…”

Section: Introductionmentioning

confidence: 99%

Chaotic Resonance in Typical Routes to Chaos in the Izhikevich Neuron Model

Nobukawa

Nishimura

Yamanishi

2017

Sci Rep

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Chaotic resonance (CR), in which a system responds to a weak signal through the effects of chaotic activities, is a known function of chaos in neural systems. The current belief suggests that chaotic states are induced by different routes to chaos in spiking neural systems. However, few studies have compared the efficiency of signal responses in CR across the different chaotic states in spiking neural systems. We focused herein on the Izhikevich neuron model, comparing the characteristics of CR in the chaotic states arising through the period-doubling or tangent bifurcation routes. We found that the signal response in CR had a unimodal maximum with respect to the stability of chaotic orbits in the tested chaotic states. Furthermore, the efficiency of signal responses at the edge of chaos became especially high as a result of synchronization between the input signal and the periodic component in chaotic spiking activity.

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Section: Introductionmentioning

confidence: 99%

Chaotic Resonance in Typical Routes to Chaos in the Izhikevich Neuron Model

Nobukawa

Nishimura

Yamanishi

2017

Sci Rep

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“…The observed phase synchronization profile for coupled bursting neurons are similar to those observed in Kuramoto oscillators. Our analysis show that if the frequency distribution of Kuramoto oscillators is properly defined, then both models can describe the same phase synchronization transition [8]. In this paper, we describe in details the method to generate such equivalence.…”

Section: Introductionmentioning

confidence: 99%

Building phase synchronization equivalence between coupled bursting neurons and phase oscillators

Ferrari

Viana

2018

J. Phys. Commun.

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Bursting neurons are characterized by an alternation of active and inactive state, during the active state they exhibit train of spikes and quiescent behavior in the inactive state. When bursting neurons are coupled they can synchronize depending on the coupling strength. If the coupling strength is increased above a critical value, a transition from an asynchronous state to a partial synchronized state can be observed. This transition has the same type observed in coupled Kuramoto oscillators. When the natural frequency distribution of the oscillators is properly defined, the bursting neurons and the Kuramoto oscillators describe the same phase transition for synchronization.

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“…This kind of SFNs are inhomogeneous ones with a few "hubs" (superconnected nodes), in contrast to statistically homogeneous networks such as random graphs and small-world networks [56,57]. Many recent works on various subjects of neurodynamics (e.g., coupling-induced burst synchronization, delay-induced burst synchronization, and suppression of burst synchronization) have been done in SFNs with a few percent of hub neurons with an exceptionally large number of connections [58][59][60][61][62][63].…”

Section: Introductionmentioning

confidence: 99%

Effect of network architecture on burst and spike synchronization in a scale-free network of bursting neurons

Kim

Lim

2016

Neural Networks

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We investigate the effect of network architecture on burst and spike synchronization in a directed scale-free network (SFN) of bursting neurons, evolved via two independent α− and β−processes.The α−process corresponds to a directed version of the Barabási-Albert SFN model with growth and preferential attachment, while for the β−process only preferential attachments between preexisting nodes are made without addition of new nodes. We first consider the "pure" α−process of symmetric preferential attachment (with the same in-and out-degrees), and study emergence of burst and spike synchronization by varying the coupling strength J and the noise intensity D for a fixed attachment degree. Characterizations of burst and spike synchronization are also made by employing realistic order parameters and statistical-mechanical measures. Next, we choose appropriate values of J and D where only the burst synchronization occurs, and investigate the effect of the scale-free connectivity on the burst synchronization by varying (1) the symmetric attachment degree and (2) the asymmetry parameter (representing deviation from the symmetric case) in the α−process, and (3) the occurrence probability of the β−process. In all these three cases, changes in the type and the degree of population synchronization are studied in connection with the network topology such as the degree distribution, the average path length L p , and the betweenness centralization B c . It is thus found that not only L p and B c (affecting global communication between nodes) but also the in-degree distribution (affecting individual dynamics) are important network factors for effective population synchronization in SFNs.

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Phase synchronization of coupled bursting neurons and the generalized Kuramoto model

Cited by 60 publications

References 81 publications

Chaotic Resonance in Typical Routes to Chaos in the Izhikevich Neuron Model

Chaotic Resonance in Typical Routes to Chaos in the Izhikevich Neuron Model

Building phase synchronization equivalence between coupled bursting neurons and phase oscillators

Effect of network architecture on burst and spike synchronization in a scale-free network of bursting neurons

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