This article investigates the emergence of phase synchronization in a network of randomly connected neurons by chemical synapses. The study uses the classic Hodgkin-Huxley model to simulate the neuronal dynamics under the action of a train of Poissonian spikes. In such a scenario, we observed the emergence of irregular spikes for a specific range of conductances, and also that the phase synchronization of the neurons is reached when the external current is strong enough to induce spiking activity but without overcoming the coupling current. Conversely, if the external current assumes very high values, then an opposite effect is observed, i.e. the prevention of the network synchronization. We explain such behaviors considering different mechanisms involved in the system, such as incoherence, minimization of currents, and stochastic effects from the Poissonian spikes. Furthermore, we present some numerical simulations where the stimulation of only a fraction of neurons, for instance, can induce phase synchronization in the non-stimulated fraction of the network, besides cases in which for larger coupling values it is possible to propagate the spiking activity in the network when considering stimulation over only one neuron.
In this paper, we investigated the neural spikes synchronisation in a neural network with synaptic plasticity and external perturbation. In the simulations the neural dynamics is described by the Hodgkin Huxley model considering chemical synapses (excitatory) among neurons. According to neural spikes synchronisation is expected that a perturbation produce non synchronised regimes. However, in the literature there are works showing that the combination of synaptic plasticity and external perturbation may generate synchronised regime. This article describes the effect of the synaptic plasticity …
For modeling complex synaptic connectivity, we consider the Watts-Strogatz small-world network which interpolates between regular lattice and random network via rewiring, and investigate the effect of small-world connectivity on emergence of noise-induced population synchronization in an inhibitory population of subthreshold bursting Hindmarsh-Rose neurons. Thus, noise-induced slow burst synchronization and fasg spike synchronization are found to appear in a synchronized region of the $J-D$ plane. As the rewiring probability $p$ is decreased from 1 (random network) to 0 (regular lattice), the …
Measures of spike train synchrony have proven a valuable tool in both experimental and computational neuroscience. Particularly useful are time-resolved methods such as the ISI- and the SPIKE-distance, which have already been applied in various bivariate and multivariate contexts. Recently, SPIKE-Synchronization was proposed as another time-resolved synchronization measure. It is based on Event-Synchronization and has a very intuitive interpretation. Here, we present a detailed analysis of the mathematical properties of these three synchronization measures. For example, we were able to obtain …
We are interested in characterization of population synchronization of bursting neurons which exhibit both the slow bursting and the fast spiking timescales, in contrast to spiking neurons. Population synchronization may be well visualized in the raster plot of neural spikes which can be obtained in experiments. The instantaneous population firing rate (IPFR) $R(t)$, which may be directly obtained from the raster plot of spikes, is often used as a realistic collective quantity describing population behaviors in both the computational and the experimental neuroscience. For the case of spiking n…
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 pre-existing 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 sy…
We analyze the time resolved spike statistics of a solitary and two mutually interacting chaotic semiconductor lasers whose chaos is characterized by apparently random, short intensity spikes. Repulsion between two successive spikes is observed, resulting in a refractory period which is largest at laser threshold. For time intervals between spikes greater than the refractory period, the distribution of the intervals follows a Poisson distribution. The spiking pattern is highly periodic over time windows corresponding to the optical length of the external cavity, with a slow change of the spiki…
Synchronized brain rhythms, associated with diverse cognitive functions, have been observed in electrical recordings of brain activity. Neural synchronization may be well described by using the population-averaged global potential $V_G$ in computational neuroscience. The time-averaged fluctuation of $V_G$ plays the role of a "thermodynamic" order parameter $\cal {O}$ used for describing the synchrony-asynchrony transition in neural systems. Population spike synchronization may be well visualized in the raster plot of neural spikes. The degree of neural synchronization seen in the raster plot i…
We are interested in characterization of synchronization transitions of bursting neurons in the frequency domain. Instantaneous population firing rate (IPFR) $R(t)$, which is directly obtained from the raster plot of neural spikes, is often used as a realistic collective quantity describing population activities in both the computational and the experimental neuroscience. For the case of spiking neurons, a realistic time-domain order parameter, based on $R(t)$, was introduced in our recent work to characterize the spike synchronization transition. Unlike the case of spiking neurons, the IPFR $…
We consider a clustered network with small-world sub-networks of inhibitory fast spiking interneurons, and investigate the effect of inter-modular connection on emergence of fast sparsely synchronized rhythms by varying both the inter-modular coupling strength $J_{inter}$ and the average number of inter-modular links per interneuron $M_{syn}^{(inter)}$. In contrast to the case of non-clustered networks, two kinds of sparsely synchronized states such as modular and global synchronization are found. For the case of modular sparse synchronization, the population behavior reveals the modular struc…
We consider an excitatory population of subthreshold Izhikevich neurons which exhibit noise-induced firings. By varying the coupling strength $J$, we investigate population synchronization between the noise-induced firings which may be used for efficient cognitive processing such as sensory perception, multisensory binding, selective attention, and memory formation. As $J$ is increased, rich types of population synchronization (e.g., spike, burst, and fast spike synchronization) are found to occur. Transitions between population synchronization and incoherence are well described in terms of an…
We observe and study a self-organized phenomenon whereby the activity in a network of spiking neurons spontaneously terminates. We consider different types of populations, consisting of bistable model neurons connected electrically by gap junctions, or by either excitatory or inhibitory synapses, in a scale-free connection topology. We find that strongly synchronized population spiking events lead to complete cessation of activity in excitatory networks, but not in gap junction or inhibitory networks. We identify the underlying mechanism responsible for this phenomenon by examining the particu…
The presence of spikes and sharp waves in the recordings of epileptic patients may contaminate background signal synchronization in different ways. In this Technical Note, we present a simple procedure for assessing whether a particular synchronization method should be used (or not) with data from neurophysiological recordings commonly used to evaluate epilepsy. The information provided by this procedure makes it possible to differentiate true background synchronization from spike synchronization. This issue is particularly relevant when differentiating between the mechanisms underlying the on…
We are concerned about burst synchronization (BS), related to neural information processes in health and disease, in the Barabási-Albert scale-free network (SFN) composed of inhibitory bursting Hindmarsh-Rose neurons. This inhibitory neuronal population has adaptive dynamic synaptic strengths governed by the inhibitory spike-timing-dependent plasticity (iSTDP). In previous works without considering iSTDP, BS was found to appear in a range of noise intensities for fixed synaptic inhibition strengths. In contrast, in our present work, we take into consideration iSTDP and investigate its effect o…
We consider an excitatory population of subthreshold Izhikevich neurons which cannot fire spontaneously without noise. As the coupling strength passes a threshold, individual neurons exhibit noise-induced burstings. This neuronal population has adaptive dynamic synaptic strengths governed by the spike-timing-dependent plasticity (STDP). In the absence of STDP, stochastic burst synchronization (SBS) between noise-induced burstings of subthreshold neurons was previously found to occur over a large range of intermediate noise intensities. Here, we study the effect of additive STDP on the SBS by v…
We consider clustered small-world networks with both inhibitory (I) and excitatory (E) populations. This I-E neuronal network has adaptive dynamic I to E and E to I interpopulation synaptic strengths, governed by interpopulation spike-timing-dependent plasticity (STDP). In previous works without STDPs, fast sparsely synchronized rhythms, related to diverse cognitive functions, were found to appear in a range of noise intensity $D$ for static synaptic strengths. By varying $D$, we investigate the effect of interpopulation STDPs on diverse population and individual properties of fast sparsely sy…
Techniques for recording large-scale neuronal spiking activity are developing very fast. This leads to an increasing demand for algorithms capable of analyzing large amounts of experimental spike train data. One of the most crucial and demanding tasks is the identification of similarity patterns with a very high temporal resolution and across different spatial scales. To address this task, in recent years three time-resolved measures of spike train synchrony have been proposed, the ISI-distance, the SPIKE-distance, and event synchronization. The Matlab source codes for calculating and visualiz…
We study the synchronization of two model neurons coupled through a synapse having an activity-dependent strength. Our synapse follows the rules of Spike-Timing Dependent Plasticity (STDP). We show that this plasticity of the coupling between neurons produces enlarged frequency locking zones and results in synchronization that is more rapid and much more robust against noise than classical synchronization arising from connections with constant strength. We also present a simple discrete map model that demonstrates the generality of the phenomenon.
An analytical description of the response properties of simple but realistic neuron models in the presence of noise is still lacking. We determine completely up to the second order the firing statistics of a single and a pair of leaky integrate-and-fire neurons (LIFs) receiving some common slowly filtered white noise. In particular, the auto- and cross-correlation functions of the output spike trains of pairs of cells are obtained from an improvement of the adiabatic approximation introduced in \cite{Mor+04}. These two functions define the firing variability and firing synchronization between …
We investigate the synchronization features of a network of spiking neurons under a distance-dependent coupling following a power-law model. The interplay between topology and coupling strength leads to the existence of different spatiotemporal patterns, corresponding to either non-synchronized or phase-synchronized states. Particularly interesting is what we call synchronization malleability, in which the system depicts significantly different phase synchronization degrees for the same parameters as a consequence of a different ordering of neural inputs. We analyze the functional connectivity…
We consider the Watts-Strogatz small-world network (SWN) consisting of inhibitory fast spiking Izhikevich interneurons. This inhibitory neuronal population has adaptive dynamic synaptic strengths governed by the inhibitory spike-timing-dependent plasticity (iSTDP). In previous works without iSTDP, fast sparsely synchronized rhythms, associated with diverse cognitive functions, were found to appear in a range of large noise intensities for fixed strong synaptic inhibition strengths. Here, we investigate the effect of iSTDP on fast sparse synchronization (FSS) by varying the noise intensity $D$.…
The coherence resonance (CR) of globally coupled Hodgkin-Huxley neurons is studied. When the neurons are set in the subthreshold regime near the firing threshold, the additive noise induces limit cycles. The coherence of the system is optimized by the noise. A bell-shaped curve is found for the peak height of power spectra of the spike train, being significantly different from a monotonic behavior for the single neuron. The coupling of the network can enhance CR in two different ways. In particular, when the coupling is strong enough, the synchronization of the system is induced and optimized …
The collective dynamics of excitatory pulse coupled neural networks with spike timing dependent plasticity (STDP) is studied. Depending on the model parameters stationary states characterized by High or Low Synchronization can be observed. In particular, at the transition between these two regimes, persistent irregular low frequency oscillations between strongly and weakly synchronized states are observable, which can be identified as infraslow oscillations with frequencies 0.02 - 0.03 Hz. Their emergence can be explained in terms of the Sisyphus Effect, a mechanism caused by a continuous feed…
Measures of multiple spike train synchrony are essential in order to study issues such as spike timing reliability, network synchronization, and neuronal coding. These measures can broadly be divided in multivariate measures and averages over bivariate measures. One of the most recent bivariate approaches, the ISI-distance, employs the ratio of instantaneous interspike intervals. In this study we propose two extensions of the ISI-distance, the straightforward averaged bivariate ISI-distance and the multivariate ISI-diversity based on the coefficient of variation. Like the original measure thes…
Conventional digital computation is rapidly approaching physical limits for speed and energy dissipation. Here we fabricate and test a simple neuromorphic circuit that models neuronal somas, axons and synapses with superconducting Josephson junctions. The circuit models two mutually coupled excitatory neurons. In some regions of parameter space the neurons are desynchronized. In others, the Josephson neurons synchronize in one of two states, in-phase or anti-phase. An experimental alteration of the delay and strength of the connecting synapses can toggle the system back and forth in a phase-fl…
We show that in model neuronal cultures, where the probability of interneuronal connection formation decreases exponentially with increasing distance between the neurons, there exists a small number of spatial nucleation centers of a network spike, from where the synchronous spiking activity starts propagating in the network typically in the form of circular traveling waves. The number of nucleation centers and their spatial locations are unique and unchanged for a given realization of neuronal network but are different for different networks. In contrast, if the probability of interneuronal c…
