The hierarchical neural network for generating an arbitrary period rhythm

The living body has various biological rhythms with different periods. The nervous system is very important as a mechanism and a control for rhythm generation. However, the detailed constitution and the operating algorithm for the system are not well known for neural physiology or anatomy. We thus propose a hierarchical neural network for generating a sine wave with an arbitrary period rhythm. The network consists of three layers, where each layer has some neural units and where the backpropagation rule (BP rule) is used. The principles of generating a rhythm are as follows. Training signals are prepared from sampling a sine wave with an arbitrary period, and these are the only external inputs. After calculating the error, the output is fed back, in sequence, to the input layer through some delaying elements. All the weights are modified by the BP rule, then the given rhythm wave appears at the output unit. We show three types of simulation, which are some period rhythms, sine waves with a superimposed triple frequency component, and noise. As the model has the ability to take external input, it is considered to correspond to the mechanism for an entrainment phenomenon.