A Novel Generalized PWC Neuron Model: Theoretical Analyses and Efficient Design of Bifurcation Mechanisms of Bursting

Abstract

A piece-wise constant (PWC) neuron model is an electronic circuit neuron model, which has a PWC vector field. In this brief, a novel generalized PWC neuron model is presented in order to reproduce fundamental bifurcation mechanisms of bursting observed in a Hodgkin-Huxley type neuron model. Thanks to the PWC vector field, the bifurcation mechanisms of the presented model can be analyzed theoretically. It is then shown that the theoretical analysis results are useful for efficient design of the presented model. A so designed model is implemented and circuit experiments validate occurrences of the bursting and the bifurcation.