A novel design method of burst mechanisms of a piece-wise constant neuron model based on bifurcation analysis

Abstract

A piece-wise constant (PWC) neuron model is an electronic circuit neuron model having a PWC vector field. In this paper, a PWC neuron model with a novel controlled voltage source is presented. Due to the nonlinearity of the voltage source, the presented model exhibits various bifurcations. Among such bifurcations, fundamental bifurcations related to burst behaviors are analyzed in this paper. Then, using the bifurcation analyses results, a novel design method of the vector field of the PWC neuron model is presented. It is shown that the presented design method enables the PWC neuron model to reproduce typical occurrence mechanisms of burst behaviors of neurons. Furthermore, the PWC neuron model is implemented as a breadboard prototype and occurrence of a typical burst behavior is validated by a real circuit experiment.