Explosive synchronization: from synthetic to real-world networks (Interdisciplinary Physics)

Synchronization is a widespread phenomenon in both synthetic and real-world networks. This collective behavior of simple and complex systems has been attracting much research during the last decades. Two different routes to synchrony are defined in networks; first-order, characterized as explosive, and second-order, characterized as continuous transition. Although pioneer researches explained that the transition type is a generic feature in the networks, recent studies proposed some frameworks in which different phase and even chaotic oscillators exhibit explosive synchronization. The relationship between the structural properties of the network and the dynamical features of the oscillators is mainly proclaimed because some of these frameworks show abrupt transitions. Despite different theoretical analyses about the appearance of the first-order transition, studies are limited to the mean-field theory, which cannot be generalized to all networks. There are different real-world and man-made networks whose properties can be characterized in terms of explosive synchronization, e.g., the transition from unconsciousness to wakefulness in the brain and spontaneous synchronization of power-grid networks. In this review article, explosive synchronization is discussed from two main aspects. First, pioneer articles are categorized from the dynamical-structural framework point of view. Then, articles that considered different oscillators in the explosive synchronization frameworks are studied. In this article, the main focus is on the explosive synchronization in networks with chaotic and neuronal oscillators. Also, efforts have been made to consider the recent articles which proposed new frameworks of explosive synchronization.

Dynamic Behavior of Coupled Neuron System from a Game-Theoretic Standpoint

This paper is concerned with the theoretical investigation of game theory concepts in analyzing the behavior of dynamically coupled oscillators. Here, we claim that the coupling strength in any neuronal oscillators can be modeled as a game. We formulate the game to describe the effect of pure-strategy Nash equilibrium on two neuron systems of Hopf-oscillator and later demonstrate the application of the same assumptions and methods to N × N neuronal sheet. We also demonstrate the effect of the proposed method on MNIST data to show the equilibrium behavior of neurons in a N × N neuronal grid for all different digits. A significant outcome of the paper is a modified Hebbian algorithm, which adapts the coupling weights to neural potential resulting in a stable phase difference. Which in turn, makes it possible for an individual neuron to encode input information.

Brain Rhythms Provide a Framework for Neural Syntax

Brain oscillations are present in the same form in all mammals and represent a fundamental aspect of neuronal computation, including the generation of movement patterns, speech, and music production. Neuronal oscillators readily entrain each other, making the exchange of messages between brain areas effective. Because all neuronal oscillations are based on inhibition, they can parse and concatenate neuronal messages, a prerequisite for any coding mechanism. This chapter discusses how the hierarchical nature of cross-frequency–coupled rhythms can serve as a scaffold for combining neuronal letters into words and words into sentences, thus providing a syntactic structure for information exchange.

Transcranial Alternating Current Stimulation (tACS) Entrains Alpha Oscillations by Preferential Phase Synchronization of Fast-Spiking Cortical Neurons to Stimulation Waveform

SummaryModeling studies predict that transcranial alternating current stimulation (tACS) entrains brain oscillations, yet direct examination has been lacking or potentially contaminated by stimulation artefact. Here we first demonstrate how the posterior parietal cortex drives primary visual cortex and thalamic LP in the alpha-band in head-fixed awake ferrets. The spike-field synchrony is maximum within alpha frequency, and more prominent for narrow-spiking neurons than broad-spiking ones. Guided by a validated model of electric field distribution, we produced electric fields comparable to those in humans and primates (< 0.5 mV/mm). We found evidence to support the model-driven predictions of how tACS entrains neural oscillations as explained by the triangular Arnold tongue pattern. In agreement with the stronger spike-field coupling of narrow-spiking cells, tACS more strongly entrained this cell population. Our findings provide the firstin vivoevidence of how tACS with electric field amplitudes used in human studies entrains neuronal oscillators.

Collective excitability in a mesoscopic neuronal model of epileptic activity

The brain can be understood as a collection of interacting neuronal oscillators, but the extent to which its sustained activity is due to coupling among brain areas is still unclear. Here we study the joint dynamics of two cortical columns described by Jansen-Rit neural mass models, and show that coupling between the columns gives rise to stochastic initiations of sustained collective activity, which can be interpreted as epileptic events. For large enough coupling strengths, termination of these events results mainly from the emergence of synchronization between the columns, and thus is controlled by coupling instead of noise. Stochastic triggering and noise-independent durations are characteristic of excitable dynamics, and thus we interpret our results in terms of collective excitability.

Effect of Phase Response Curve Shape and Synaptic Driving Force on Synchronization of Coupled Neuronal Oscillators

The role of the phase response curve (PRC) shape on the synchrony of synaptically coupled oscillating neurons is examined. If the PRC is independent of the phase, because of the synaptic form of the coupling, synchrony is found to be stable for both excitatory and inhibitory coupling at all rates, whereas the antisynchrony becomes stable at low rates. A faster synaptic rise helps extend the stability of antisynchrony to higher rates. If the PRC is not constant but has a profile like that of a leaky integrate-and-fire model, then, in contrast to the earlier reports that did not include the voltage effects, mutual excitation could lead to stable synchrony provided the synaptic reversal potential is below the voltage level the neuron would have reached in the absence of the interaction and threshold reset. This level is controlled by the applied current and the leakage parameters. Such synchrony is contingent on significant phase response (that would result, for example, by a sharp PRC jump) occurring during the synaptic rising phase. The rising phase, however, does not contribute significantly if it occurs before the voltage spike reaches its peak. Then a stable near-synchronous state can still exist between type 1 PRC neurons if the PRC shows a left skewness in its shape. These results are examined comprehensively using perfect integrate-and-fire, leaky integrate-and-fire, and skewed PRC shapes under the assumption of the weakly coupled oscillator theory applied to synaptically coupled neuron models.