Modeling of a Neural Pattern Generator with Coupled nonlinear Oscillators

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Abstract
A set of van der Pol oscillators is arranged in a network in which each oscillator is coupled to each other oscillator. Through the selection of coupling coefficients, the network is made to appear as a ring and as a chain of coupled oscillators. Each oscillator is provided with amplitude, frequency, and offset parameters which have analytically indeterminable effects on the output waves. These systems are simulated on the digital computer in order to study the amplitude, frequency, offset, and phase relationships of the waves versus parameter changes. Based on the simulations, systems of coupled oscillators are configured so that they exhibit stable patterns of signals which can be used to model the central pattern generator (CPG) of living organisms. Using a simple biped as an example locomotory system, the CPG model generates control signals for simulated walking and jumping maneuvers. It is shown that with parameter adjustments, as guided by the simulations, the model can be made to generate kinematic trajectories which closely resemble those for the human walking gait. Further-more, minor tuning of these parameters along with some algebraic sign changes of coupling coefficients can effect a transition in the trajectories to those of a two-legged hopping gait. The generalized CPG model is shown to be versatile enough that it can also generate various n-legged gaits and spinal undulatory motions, as in the swimming motions of a fish.