Stochastic Evolution Model of Neuronal Oscillator Population under the Condition of the Higher Order Coupling

The activities of coupled neuronal oscillator population in the presence of both external stimulation and noise were studied in this paper, and the dynamical evolution of the average number density of the neuronal oscillator population was studied when the coupling among oscillators contains higher harmonics. The results of the study indicate that under the condition of higher order coupling, if the initial condition of average number density contains the same harmonics with the higher order coupling and the coupling strength is greater than its critical value, the action of higher order coupling can maintain the already formed multiple-cluster synchronization state of the neuronal oscillator population. Under the condition of stimulation, the effect of phase neural coding is the correlative result of the coupling and the stimulation.