Synchronization And Stochastic Resonance Dynamics Of A Neural Network Under The Influence Of Spatially Correlated White Noise

Biological neural network system is composed by a huge number of neurons, it is information network system which topology structure is extremely complicate. The neural network system undertakes the important functions of biological feel stimulation from outside, production, processing, transmission neural signals and cognitive activities. It is well known that the noise is unavoidable in the nervous system, in order to better describe the noise environment of real neural system, spatially correlated noise has been introduced into the neural network system. Therefore, investigate the dynamics of neuronal network system subjected to spatially correlated noise is very significance. This article is based on the stochastic dynamics theory and numerical simulation method, discuss the synchronous and stochastic resonance dynamics of neuronal network system subjected to spatially correlated white noise. The main contents and conclusions are as follows:1. We have investigated the synchronous dynamics of neuronal network system subjected to spatially correlated white noise. First, by using the small-world neuronal network system, through the dynamical mean-field approximation theory the original higher dimensional stochastic differential equations of the network system are transformed to lower dimensional deterministic moment differential equations. Then, the synchronous dynamics of the original neuronal network system obtained by direct numerical simulations is compared with those obtained by the dynamical mean-field approximation theory, and good consistence between them is revealed. Furthermore, based on this set of moment differential equations, the key effects of spatially correlated noise and network structure on the synchronous firing property are discussed in neuronal network system. The results have shown that the noise spatial correlation coefficient, the coupling strength as well as the average vertex degree can play a positive role in inducing synchronous neuronal behaviors, but the increase of the number of nodes contained in the network can weaken the synchronization. Finally, through the dynamical mean-field approximation theory, we discuss the synchronous dynamics of modular neuronal network system under spatially correlated white noise.2. We investigate the nontrivial roles of spatially correlated white noise on the spatiotemporal collective behaviors of a modular neuronal network. The modular neuronal network is consisted of a NW small-world subnetwork and a BA scale-free subnetwork, and the considered network is composed of FitzHugh-Nagumo neurons. Our numerical results indicate that when such a modular network is subjected to an external subthreshold periodic signal, its collective response is optimized for an intermediate intensity of spatially correlated white noise, namely, stochastic resonance behavior can be induced by an appropriate intensity of spatially correlated white noise in the whole module neural network system. In order to better understand the resonant behavior of the entire network, we also discuss the dynamics of the individual neurons and the subnetworks. Conclusive evidence demonstrate that the stochastic resonance behavior are exist in individual neurons and module of the network. Further, we find that the structure of NW small-world subnetwork is more beneficial than it of BA scale-free subnetwork for stochastic resonance behavior of modular neuronal network. Meanwhile, the NW subnetwork is easier to obtain stochastic resonance than BA subnetwork. Furthermore, above phenomena are robust to changes of the noise spatially correlation coefficient and the intraconnection probability of NW subnetwork.