Collective Almost Synchronisation in Complex Networks

Baptista, Murilo S.; Ren, Hai‐Peng; Swarts, J. C. M.; Carareto, Rodrigo; Nijmeijer, Henk; Grebogi, Celso

doi:10.1371/journal.pone.0048118

Cited by 13 publications

(18 citation statements)

References 45 publications

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“…In this work, we show that the Hindmarsh-Rose neuron networks, with both chemical and electrical couplings and operating25 in a regime that exhibits the so called Collective Almost Synchronisation (CAS), produces an output signal that model very well the EEG signal recorded from four randomly selected regions of the brain. The model is therefore neither subject dependent nor region dependent.…”

Section: Discussionmentioning

confidence: 99%

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Weak connections form an infinite number of patterns in the brain

Ren

Bai

Baptista

et al. 2017

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Recently, much attention has been paid to interpreting the mechanisms for memory formation in terms of brain connectivity and dynamics. Within the plethora of collective states a complex network can exhibit, we show that the phenomenon of Collective Almost Synchronisation (CAS), which describes a state with an infinite number of patterns emerging in complex networks for weak coupling strengths, deserves special attention. We show that a simulated neuron network with neurons weakly connected does produce CAS patterns, and additionally produces an output that optimally model experimental electroencephalograph (EEG) signals. This work provides strong evidence that the brain operates locally in a CAS regime, allowing it to have an unlimited number of dynamical patterns, a state that could explain the enormous memory capacity of the brain, and that would give support to the idea that local clusters of neurons are sufficiently decorrelated to independently process information locally.

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Section: Discussionmentioning

confidence: 99%

“…The conventional wisdom is that the neurons are completely disordered when coupling strength is very weak. However, a recent research work25 shows that CAS is present in complex networks for very weak coupling strengths. In this situation, the neuron networks can process an infinite number of possible oscillatory patterns.…”

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confidence: 98%

Weak connections form an infinite number of patterns in the brain

Ren

Bai

Baptista

et al. 2017

Sci Rep

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“…Thus, for weak couplings, partial synchronization is favored by these newly formed local connections, while higher couplings are required to overcome the long distances created so that r ∼ 1 is reached [100][101][102]104]. It is also important to remark that the emergence of non vanishing synchronization for small coupling strengths might be due to the existence of relatively constant local mean-fields produced by nodes evolving around periodic stable orbits, a phenomenon called collective almost synchronization [105].…”

Section: Network With Non-vanishing Transitivitymentioning

confidence: 99%

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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“…Synchronisation phenomenon was recognised by Huygens in the 17th century, time when he performed experiments to understand this phenomenon [2]. To date, several kinds of synchronisation among coupled systems were reported, such as complete [3], phase [4,5], lag [6], and collective almost synchronisation [7]. Neuronal synchronous rhythms have been observed in a wide range of researches about cognitive functions [8,9].…”

Section: Introductionmentioning

confidence: 99%

Synchronised firing patterns in a random network of adaptive exponential integrate-and-fire neuron model

et al. 2017

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We have studied neuronal synchronisation in a random network of adaptive exponential integrate-and-fire neurons. We study how spiking or bursting synchronous behaviour appears as a function of the coupling strength and the probability of connections, by constructing parameter spaces that identify these synchronous behaviours from measurements of the inter-spike interval and the calculation of the order parameter. Moreover, we verify the robustness of synchronisation by applying an external perturbation to each neuron. The simulations show that bursting synchronisation is more robust than spike synchronisation.

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Collective Almost Synchronisation in Complex Networks

Cited by 13 publications

References 45 publications

Weak connections form an infinite number of patterns in the brain

Weak connections form an infinite number of patterns in the brain

The Kuramoto model in complex networks

Synchronised firing patterns in a random network of adaptive exponential integrate-and-fire neuron model

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