Study On Neuronal Network Under Pairwise Correlated Inputs

Neurons live in a noisy environment,wherein there are two main classes of the noises:synaptic noise and channel noise,and the synaptic noise can be moreover classified into external synaptic noise and internal synaptic noise.The external synaptic noise used to be modelled by a family of independent stochastic processes,while such approach discards its more complex statistical properties,such as correlation.Therefore,it is necessary to consider the impacts of the correlation of the external synaptic noise.The model that we consider is a Hodgkin-Huxely neuronal network driven by external synaptic noise,internal synaptic noise and channel noise.Here,the external synaptic noise is a family of pairwise-correlated stochastic processes—single interaction Poisson processes(SIP),the internal synaptic noise is generated by the random connection of the internal neurons,and the channel noise is approximated by a diffusion process.For such a complex system,we adopt Euler-Maruyama method for numerical simula-tion,and the data obtained by the simulation are used for firing statistics of the neuronal network.Firstly,we discard the internal random connection,then find the impacts of the intensity and pairwise correlation coefficient of the SIP inputs on the firing behaviours of uncoupled neuronal network.Secondly,we consider the internal random connection,then conclude the joint action of the synaptic connection probability,the intensity and pairwise correlation coefficient of the SIP inputs,on the coupled neuronal network.