Phase Synchronization Of Delay-coupled Neuronal Oscillator Population Under Periodic Stimulus

The neural system consists of various neuronal populations.Experiment shows that there is a strong correlation between synchronous firing activity and neural information transfer in the neural system.Over synchronization or loss of synchronization can lead to neural diseases in neural system.The existence of synaptic cleft and the finite propagation of signal may lead to time delay.Neural system is inevitably influenced by periodic stimulus and noise.So it's important to study how periodic stimulus?noise and time delay influence the synchronization dynamics of coupled neuronal populations in order to understand the information processing of neural system.In this paper,the phase model of time-delayed coupled neuronal oscillators population in the presence of periodic stimulus is proposed.And the evolution equation of average number density describing the overall activity of neuronal population is derived with the Fokker-Planck equation.Firstly,we study the effect of periodic stimulus and noise on synchronization activity of neural population.The results show that the impact of stimulus on synchronization of a population of neuronal oscillators depends on stimulation intensity and stimulation frequency.If stimulus frequency is much smaller or larger than the characteristic frequency of system,the number density of neuronal population shows a damped oscillation behavior.If the stimulus frequency is close to the characteristic frequency of system,the neuronal population tends to complete synchronization.As the stimulus frequency is fixed,stimulus with stronger intensity leads to higher synchronization.Moreover,the increase of noise intensity will repress the oscillatory synchronization activity of neuronal oscillator population.Then,we study the firing patterns of time-delayed coupled neuronal oscillator population in the presence of periodic stimulus.We first analyze the synchronization activity of neural population without external stimulus.Numerical results indicate that the number density of neural oscillator population presents a synchronous oscillatory with the amplitude decreasing,and the bigger the time delay,the higher the degree of synchronization.Then we further consider the firing patterns of time-delayed neuronal oscillator population in the presence of periodic stimulus.The results are described as follow.If stimulus frequency is much smaller than the characteristic frequency of system,changing stimulus intensity will alter the synchronization firing patterns.Timedelay can strength the synchronization degree of neural population with a weak stimulus,while the time delay doesn't affect the behavior of neuronal population with a stronger stimulus.If the stimulus frequency is close to the characteristic frequency of system,synchronization activity of neuronal population is dominated by stimulus intensity under the condition of a weak stimulus,while the synchronization activity is simultaneously dominated by stimulus intensity and time delay under the condition of a strong stimulus.