Propagation of firing rate in a feed-forward neuronal network (original) (raw)
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Synchronization and Inter-Layer Interactions of Noise-Driven Neural Networks
Frontiers in computational neuroscience, 2017
In this study, we used the Hodgkin-Huxley (HH) model of neurons to investigate the phase diagram of a developing single-layer neural network and that of a network consisting of two weakly coupled neural layers. These networks are noise driven and learn through the spike-timing-dependent plasticity (STDP) or the inverse STDP rules. We described how these networks transited from a non-synchronous background activity state (BAS) to a synchronous firing state (SFS) by varying the network connectivity and the learning efficacy. In particular, we studied the interaction between a SFS layer and a BAS layer, and investigated how synchronous firing dynamics was induced in the BAS layer. We further investigated the effect of the inter-layer interaction on a BAS to SFS repair mechanism by considering three types of neuron positioning (random, grid, and lognormal distributions) and two types of inter-layer connections (random and preferential connections). Among these scenarios, we concluded th...
Firing synchronization and temporal order in noisy neuronal networks
Cognitive Neurodynamics, 2008
Noise-induced complete synchronization and frequency synchronization in coupled spiking and bursting neurons are studied firstly. The effects of noise and coupling are discussed. It is found that bursting neurons are easier to achieve firing synchronization than spiking ones, which means that bursting activities are more important for information transfer in neuronal networks. Secondly, the effects of noise on firing synchronization in a noisy map neuronal network are presented. Noise-induced synchronization and temporal order are investigated by means of the firing rate function and the order index. Firing synchronization and temporal order of excitatory neurons can be greatly enhanced by subthreshold stimuli with resonance frequency. Finally, it is concluded that random perturbations play an important role in firing activities and temporal order in neuronal networks.
Synchronization in a noise-driven developing neural network
Physical Review E, 2011
We use computer simulations to investigate the structural and dynamical properties of a developing neural network whose activity is driven by noise. Structurally, the constructed neural networks in our simulations exhibit the small-world properties that have been observed in several neural networks. The dynamical change of neuronal membrane potential is described by the Hodgkin-Huxley model, and two types of learning rules, including spike-timing-dependent plasticity (STDP) and inverse STDP, are considered to restructure the synaptic strength between neurons. Clustered synchronized firing (SF) of the network is observed when the network connectivity (number of connections/maximal connections) is about 0.75, in which the firing rate of neurons is only half of the network frequency. At the connectivity of 0.86, all neurons fire synchronously at the network frequency. The network SF frequency increases logarithmically with the culturing time of a growing network and decreases exponentially with the delay time in signal transmission. These conclusions are consistent with experimental observations. The phase diagrams of SF in a developing network are investigated for both learning rules.
Optical Memory and Neural Networks, 2010
Synchronization plays important role in generation of brain activity patterns. Experimental data show that neurons demonstrate more reproducible activity for noise-like input than for constant current injection, and that effect can not be reproduced by standard oversimplified Firing-Rate (FR) models. The paper proposes a modification of FR model which reproduces these kinds of activity. The FR model approximates the firing rate of an infinite number of leaky integrate-and-fire neurons, considered as a population, and in contrary to conventional models it accounts for not only a steady-state firing regime but a fast rising excitation as well. Comparison of our simulations with the experimental data shows that the synchronous firing of the neuronal population strongly depends on the synchrony of neuronal states just before spiking. This effect is reproduced by the proposed FR model in contrary to the conventional FR models and is in agreement with the direct Monte-Carlo simulation of individual neurons.
Synchronization in a network of model neurons
Physical Review E, 2007
We study the spatiotemporal dynamics of a network of coupled chaotic maps modelling neuronal activity, under variation of coupling strength ⑀ and degree of randomness in coupling p. We find that at high coupling strengths ͑⑀ Ͼ ⑀ fixed ͒ the unstable saddle point solution of the local chaotic maps gets stabilized. The range of coupling where this spatiotemporal fixed point gains stability is unchanged in the presence of randomness in the connections, namely ⑀ fixed is invariant under changes in p. As coupling gets weaker ͑⑀ Ͻ ⑀ fixed ͒, the spatiotemporal fixed point loses stability, and one obtains chaos. In this regime, when the coupling connections are completely regular ͑p =0͒, the network becomes spatiotemporally chaotic. Interestingly however, in the presence of random links ͑p Ͼ 0͒ one obtains spatial synchronization in the network. We find that this range of synchronized chaos increases exponentially with the fraction of random links in the network. Further, in the space of fixed coupling strengths, the synchronization transition occurs at a finite value of p, a scenario quite distinct from the many examples of synchronization transitions at p → 0. Further we show that the synchronization here is robust in the presence of parametric noise, namely in a network of nonidentical neuronal maps. Finally we check the generality of our observations in networks of neurons displaying both spiking and bursting dynamics.
Acta Mechanica Sinica, 2008
Recent advances in the experimental and theoretical study of dynamics of neuronal electrical firing activities are reviewed. Firstly, some experimental phenomena of neuronal irregular firing patterns, especially chaotic and stochastic firing patterns, are presented, and practical nonlinear time analysis methods are introduced to distinguish deterministic and stochastic mechanism in time series. Secondly, the dynamics of electrical firing activities in a single neuron is concerned, namely, fast-slow dynamics analysis for classification and mechanism of various bursting patterns, one-or two-parameter bifurcation analysis for transitions of firing patterns, and stochastic dynamics of firing activities (stochastic and coherence resonances, integer multiple and other firing patterns induced by noise, etc.).
Effects of firing synchrony on signal propagation in layered networks
Spiking neurons which integrate to threshold and fire were used to study the transmission of frequency modulated (FM) signals through layered networks. Firing correlations between cells in the input layer were found to modulate the transmission of FM signals under certain dynamical conditions. A tonic level of activity was maintained by providing each cell with a source of Poissondistributed synaptic input. When the average membrane depolarization produced by the synaptic input was sufficiently below threshold, the firing correlations between cells in the input layer could greatly amplify the signal present in subsequent layers. When the depolarization was sufficiently close to threshold, however, the firing synchrony between cells in the initial layers could no longer effect the propagation of FM signals. In this latter case, integrateand-fire neurons could be effectively modeled by simpler analog elements governed by a linear input-output relation.
Emergence of synchronization and regularity in firing patterns in time-varying neural hypernetworks
Physical Review E, 2018
We study synchronization of dynamical systems coupled in time-varying network architectures, composed of two or more network topologies, corresponding to different interaction schemes. As a representative example of this class of time-varying hypernetworks, we consider coupled Hindmarsh-Rose neurons, involving two distinct types of networks, mimicking interactions that occur through the electrical gap junctions and the chemical synapses. Specifically, we consider the connections corresponding to the electrical gap junctions to form a small-world network, while the chemical synaptic interactions form a unidirectional random network. Further, all the connections in the hypernetwork are allowed to change in time, modeling a more realistic neurobiological scenario. We model this time variation by rewiring the links stochastically with a characteristic rewiring frequency f. We find that the coupling strength necessary to achieve complete neuronal synchrony is lower when the links are switched rapidly. Further, the average time required to reach the synchronized state decreases as synaptic coupling strength and/or rewiring frequency increases. To quantify the local stability of complete synchronous state we use the Master Stability Function approach, and for global stability we employ the concept of basin stability. The analytically derived necessary condition for synchrony is in excellent agreement with numerical results. Further we investigate the resilience of the synchronous states with respect to increasing network size, and we find that synchrony can be maintained up to larger network sizes by increasing either synaptic strength or rewiring frequency. Last, we find that time-varying links not only promote complete synchronization, but also have the capacity to change the local dynamics of each single neuron. Specifically, in a window of rewiring frequency and synaptic coupling strength, we observe that the spiking behavior becomes more regular.
Model of the propagation of synchronous firing in a reduced neuron network
1999
We studied the spread of synchronous repetitive firing in an array of purely excitatory neurons. The network consisted of an array of up to 250× 250 neurons connected locally. We used a modified Rinzel's model for single neurons. Each neuron was connected with two neurons randomly chosen from eight neighbors. We determined the parameters of a network model needed to reproduce synchronized activity in locally connected neurons.