Phase-response Synchronization In Coupled Neuronal Population With Time Delay

The neural system consists of various neuronal populations.Experiment shows that there is a strong correlation between the synchronization dynamic behavior and neural information transmission in the neural system.In the nervous system.There is a time delay in the information transmission from the neuronal of pre-synapse to the neuronal of post-synapse,At the same time the real world will also be affected by external periodic stimulation and noise.So it's important to study how time delay,stimulus influence the synchronization dynamic behavior of coupled neuronal populations in order to understand the information transmission of neural system.The article mainly discussed two aspects of synchronization dynamic behavior in neuronal systems.On one hand,We proposed a dynamical evolution model of population of coupled neuronal oscillators in the presence of external periodic stimulus and noise,and used average number density describe the synchronized activity of the population of neuronal oscillators and derived the evolution equation of average number density.To study the external stimulation effects on the population of neuronal oscillators of discharge behavior.On the other hand,the model is introduced into time delay and the phase response curve to study external stimulation and noise is how to influence firing activity of neuronal populations.Results indicate that the time delay influenced the synchronous activity of the neuronal oscillator population.As the time delay increased,neuronal population shows stable periodic synchronous oscillation and the degree of synchronization decreased.As the stimulus intensity increased,the synchronization degree of the neuronal population increased,As the stimulus frequency increased,the synchronization degree of the neuronal population decreased rapidly,As the stimulus frequency is close to the population characteristic frequency,the synchronization degree of the neuronal population increased.