The Resonance Dynamics Of The Modular Neuron Network Under The Influence Of The Synapse

Autapse is a self-feedback structure formed by the neurons themselves,which is ubiquitous in the nervous system.Because of the noise is inevitable in the nervous system,so as to better describe the noise environment of real neural system bounded noise has been introduced into the neural network system.The neurons in the nervous system are usually different in morphology and function,which makes the parameter heterogeneity in the neural network model unavoidable.In addition,time delay effects cannot be ignored in the transmission of neural information between coupled neurons.Based on the theories and methods of the existing research results of neuroscience,we use the methods of numerical simulation,by constructing a neural network closer to the real nervous system,aimy to study the resonance dynamics of modular neuronal network with autapse and discuss the significant influence of bounded noise,parameter heterogeneity and coupling delay on the resonance dynamics.1.By constructing a model of modular neuronal network whose individual elements are FitzHugh-Nagumo(FHN)neurons,the subnetworks are NW small-world netwok and BA scale-free networks.Investigating the nontrivial effects of electrical autapse on stochastic resonance in a modular neuronal network subjected to bounded noise.Numerical simulations have demonstrated that bounded noise with proper level of amplitude can induce stochastic resonance.When autapse are introduced,for a specific range of autaptic strength multiple stochastic resonances can be induced when the autaptic time delays are appropriately adjusted.Further research found that these appropriately adjusted delays are detected to nearly approach integer multiples of the period of external weak signal when the autaptic strength is very near zero,otherwise,they do not match the period of external weak signal when the autaptic strength is slightly greater than zero.Surprisingly,in both cases the differences between arbitrary two adjacent adjusted autaptic delays always approximately equal to the period of the weak signal.The phenomenon of autaptic delay induced multiple stochastic resonances is further confirmed to be robust against the period of external weak signal and the intramodule probability of subnetwork.2.Considering the time delay effect in the transmission of neural information between coupled neurons,constructing a modular neuronal network with electrical autapse and coupling delay,we investigate the combined effects of autapse and coupling delay on the resonance dynamics of this modular neuronal network subjected to bounded noise.It is found that bounded noise with proper level of amplitude can induce stochastic resonance,moreover,the noise induced resonance dynamics can be significantly shaped by the autapse and coupling delay.In detail,when the coupling delays are integer multiples of the oscillation period of the weak signal,for a specific range of autaptic strength stochastic resonance can appear intermittently as the autaptic delays is increased and the resonance appear at the integer multiples of the oscillation period of the weak signal.However,autaptic delay can not induce multiple stochastic resonances even though with proper autaptic strength when the coupling delays are not integer multiple of the oscillation period of the weak signal.In addition,the phenomenon of autaptic delay induced multiple stochastic resonances is further confirmed to be robust against the period of weak signal and the intramodule probability of subnetwork.3.Constructing a model of modular neuronal network with chemical autapse and parameter heterogeneity,we investigate the effects of chemical autapse on the resonance dynamics of modular neuronal network with parameter heterogeneity.It is found that resonance can be induced by an appropriate level of parameter heterogeneity,moreover,for a specific range of autaptic strength multiple resonances can appear when the autaptic time delays are located at integer multiples of the oscillation period of the weak signal.Besides,the phenomenon of multiple resonances is further confirmed to be robust against the period of weak signal and the intramodule probability of subnetwork.