Summary
International Symposium on Nonlinear Theory and Its Applications
2016
Session Number:A3L-D
Session:
Number:A3L-D-4
Homoclinic Bifurcations in a Piece-Wise Constant Neuron Model
Chiaki Matsuda, Hiroyuki Torikai,
pp.-
Publication Date:2016/11/27
Online ISSN:2188-5079
Summary:
A piece-wise constant (PWC) neuron model has a piece-wise constant vector field and has been designed to mimic bifurcations of neurons, e.g., design methods of bifurcations of neural resting states (equilibrium points) have been studied. On the other hand, in this paper, we present design methods of bifurcations of neural bursting states (periodic orbits) of the PWC neuron model. It is shown that, under appropriate designs of the vector field, the PWC neuron model can exhibit bifurcations of homoclinic periodic orbits that are typically observed in neuron models with smooth vector fields. Also, occurrences of the designed bifurcations are validated in a real circuit.