Numerical analysis of a neural oscillator for periodic behaviour

Abstract

In this study, the relation between a behavior of a neural oscillator with a feedback signal and the coefficient parameters were analyzed numerically. Especially, regular sin waves were used as a feedback signal. Under this condition, the period T_N and amplitude A_N of the output signal from the neural oscillator were evaluated for a_ij and T_a /T_r as coefficient parameters, f_b as feedback parameter and T as the period of the sin wave. As a result, the period T_N got longer, when a_ij was increased or T_a /T_r was decreased. Also, when the feedback parameter f_b was increased, the output signal from the neural oscillator tended to be stable. The distribution of the period T_N related to a_ij and T_a /T_r was divided into three areas; similar, twice and unstable period areas compared to the period T of the feedback sin wave. The boundaries of the three areas were separated clearly. For the amplitude A_N of the output signal from the neural oscillator, although the distribution of the amplitude A_N showed a similar tendency to the period T_N, the boundaries were varied continuously. Based on our results, the feedback coefficient f_b could be decided to be larger in order to spread the stable areas. Then, the coefficient parameters a_ij and T_a /T_r could be decided to satisfy the required period T_N and amplitude A_N with avoiding the boundaries the areas.