Summary
International Symposium on Nonlinear Theory and its Applications
2010
Session Number:C1L-C
Session:
Number:C1L-C2
Bifurcation Analysis of Coupled Nagumo-Sato Models
Kazutoshi Kinoshita, Tetsushi Ueta, Jun’ichi Imura, Kazuyuki Aihara,
pp.488-491
Publication Date:2010/9/5
Online ISSN:2188-5079
Summary:
The Nagumo-Sato model is one of mathematical neuron models described by a piecewise linear difference equation. Since there is a conditional character which is discontinuous at the threshold value, the system can be classified as a hybrid dynamical system. Bifurcation phenomena are occurred by changing internal parameters and chaotic attractors are also given. The dynamical properties were exactly studied analytically. In this paper, we investigate the bifurcations of diffusively-coupled Nagumo-Sato models. By using complementarity a shooting algorithm and brute-force method, complete bifurcation diagrams are obtained. In spite of the discontinuities inside the coupled system, our shooting method can solve bifurcation problems. A period-locking regions edged by border-collision bifurcation sets are found, and chaotic regions are distinguished by a tangent bifurcation. We discuss on changing bifurcation structures with parameter variations.