The Cluster Firing Dynamics Characteristics Of A Neuronal Network With A Synaptic Plasticity Module

About 100 billion neurons in the cerebral cortex connect with each other through synapses and other physiological structures to constitute a complex neural network system.The brain processing of neural information is collaborative ly completed through a large number of neurons in different brain regions,so synchronous activity between neurons in the neural information processing plays an important role.On the other hand,experiments have confirmed that not all synchronous behaviors are beneficial.Abnormal synchronization of damaged brain cells usually leads to some neurophysiological diseases,such as Parkinson,primary tremor and epilepsy.Seeking reasonable de-synchronization control methods is of great significance for the prevention and treatment of neurological physiological diseases.At the same time,the intensity of synaptic transmission information in biological neural network is variable,thus synaptic plasticity is also a factor that cannot be ignored in neural network system.Motivated by these findings,this paper,based on combining the technique of neurodynamics and complex networks,constructs a modular neuronal network with synaptic plasticity and then study the bursting dynamics and synchronous control by using statistical analysis and numerical simulation.The main contents and conclusions of this paper are as follows:1.This paper explores the bursting synchronization and excitatory characteristics of the modular neuronal network with synaptic plasticity.First,we build a modular neuronal network,whose nodes are Rulkov neurons and the topology of each subnetwork is of NW small-world properties.The synaptic plasticity between coupled neurons is described by an improved Oja's learning rule.Secondly,by introducing the key factors such as order parameters,the variance of mean field and average bursting frequency,the influence of coupling strength and synaptic learning rate on the bursting dynamics of modular neuronal network is explored by numerical simulation.The results show that,large coupling strength can induce modular network to realize bursting synchronization when the synaptic weights of neurons keep unchanged.This phenomenon is robust to the parameter changes of the Rulkov map.When the synaptic weight keep updated with time,it is found that the synaptic learning rate can regulate the excitatory and bursting synchronization of the coupled neurons:With the increase of learning rate,the bursting synchronization characteristics of the modular network gradually disappear.On the contrary,the excitatory activity of the neurons is enhanced and the level of excitability will eventually remain within a reasonable range.2.The problem of synchronous control is studied in the modular neuronal network with synaptic plasticity.By constructing a discrete Courbage-Nekorkin-Vdovin(CNV)modular neural network model,the numerical results show that the coupled neurons can achieve strongly bursting synchronization when the coupling strength is large enough.Because some neuropathological state is related to the excessive synchronous firing rhythm of coupled neurons,effective synchronization control technology is proposed to suppress bursting synchronization in modular neural networks.Firstly how the synaptic plasticity controls bursting synchronization of the modular network is investigated.The results show that larger learning rate can effectively eliminate the bursting synchronization,but smaller learning rate can't suppress the bursting rhythm of neurons.Then the nonlinear time delay feedback control technology,which includes differential feedback control and direct feedback control,is further proposed to control bursting synchronization of modular neuronal network.By analyzing the inhibitory factors,the results show that the differential feedback control and direct feedback control can significantly eliminate bursting synchronization when the parameter values of feedback strength and feedback delay are adjusted appropriately.In the case of differential feedback control,the control domain of effective synchronization suppression is characterized by a semi-elliptical domain in the parameter space.For the direct feedback control,the effective control domain is characterized by a fan-shaped parameter domain.