2022 Volume 17 Issue 4 Pages 22-00124
Neural oscillators, which are a mathematical model of a central pattern generator, have been used to investigate human gait and control mobile robots. A typical neural oscillator uses two neurons that mutually inhibit each other’s activity. The exact orbitally-stable conditions of the neural activity of neural oscillators without external signals have been reported. However, the behavior of neural oscillators with external signals is unclear because their neural activity depends on the external signals, which have many types. In this study, for simplicity, external signals were regarded as a sinusoidal wave with a period Tex and an amplitude Aex. The connectivity aij, ratio for time constants τz/τx, and fatigue coefficient b were changed for neurons i and j, while Tex and Aex were changed for external signals. The orbit-stability of the output signals from a neuron was decided based on the transient time (≦ 3 s) and the duration (≧ 30 s). The period Tout and the amplitude Aout of the output signals were evaluated. Tout had discrete values of Tex, 2Tex, or 0.5Tex or was non-orbitally-stable (value of 0). When Aex was greater than or equal to ui, the neural oscillator became synchronized. For a small Tex, some combinations of τz/τx and aij values led to instability. For a large Tex, some combinations of b and aij values led to instability. In contrast to Tout, the amplitude Aout of the output signal showed continuous changes depending on τz/τx, b, and aij. The amplitude Aout could be expressed as the sum of ui and Aex. Aout was not significantly affected by τz/τx but decreased with decreasing b.