Effects of external signals on neural oscillator stability

Abstract

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 T ex and an amplitude A ex . The connectivity a i j , ratio for time constants τ z /τ x , and fatigue coefficient b were changed for neurons i and j, while T ex and A ex 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 T out and the amplitude A out of the output signals were evaluated. T out had discrete values of T ex , 2T ex , or 0.5T ex or was non-orbitally-stable (value of 0). When A ex was greater than or equal to u i , the neural oscillator became synchronized. For a small T ex , some combinations of τ z /τ x and a i j values led to instability. For a large T ex , some combinations of b and a i j values led to instability. In contrast to T out , the amplitude A out of the output signal showed continuous changes depending on τ z /τ x , b, and a i j . The amplitude A out could be expressed as the sum of u i and A ex . A out was not significantly affected by τ z /τ x but decreased with decreasing b.