Theoretical and Evolutionary Parameter Tuning of Neural Oscillators with a Double-Chain Structure for Generating Rhythmic Signals

A neural oscillator with a double-chain structure is one of the central pattern generator models used to simulate and understand rhythmic movements in living organisms. However, it is difficult to reproduce desired rhythmic signals by tuning an enormous number of parameters of neural oscillators. In this study, we propose an automatic tuning method consisting of two parts. The first involves tuning rules for both the time constants and the amplitude of the oscillatory outputs based on theoretical analyses of the relationship between parameters and outputs of the neural oscillators. The second involves an evolutionary tuning method with a two-step genetic algorithm (GA), consisting of a global GA and a local GA, for tuning parameters such as neural connection weights that have no exact tuning rule. Using numerical experiments, we confirmed that the proposed tuning method could successfully tune all parameters and generate sinusoidal waves. The tuning performance of the proposed method was less affected by factors such as the number of excitatory oscillators or the desired outputs. Furthermore, the proposed method was applied to the parameter-tuning problem of some types of artificial and biological wave reproduction and yielded optimal parameter values that generated complex rhythmic signals in Caenorhabditis elegans without trial and error.