Summary

Proceedings of the 2012 International Symposium on Nonlinear Theory and its Applications

2012

Session Number:D2L-A

Session:

Number:840

Bifurcation of Chaos and Density Spectrum of Inter-Spike-Intervals from Piecewise-Constant Spike Oscillator

Takahiro Aoki,  Tadashi Tsubone,  

pp.840-843

Publication Date:

Online ISSN:2188-5079

DOI:10.15248/proc.1.840

PDF download (618KB)

Summary:
In this study, we focus on a spike oscillator with chaotic motion governed by piecewise-constant vector field. The spike oscillator exhibits bifurcation of chaos referred to as distinguishing phenomena called “Island” which is chaos whose support of invariant measure is divided into union of subintervals in the domain of the return map. On the other hand, the oscillator generates various chaotic spike train. The density spectrum of inter-spike-intervals undergo a characteristic change depending on the parameters, that is, bifurcation phenomena on density spectrum is observed. This paper derives an existence region of Island and shows the bifurcation set of chaos on a parameter space and density spectrum analytically. Almost complete analysis of bifurcation phenomena on density spectrum of inter-spike-intervals is provided.

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