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ISSN : 1226-0657

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Vol.9 No.1
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A CONDITION OF UNIQUENESS AND STABILITY IN ABURSTING MODEL

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2002, v.9 no.1, pp.19-30
Lee, Eui-Woo
Lee,, E. (2002). A CONDITION OF UNIQUENESS AND STABILITY IN ABURSTING MODEL. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 9(1), 19-30.
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Abstract

We consider one class of bursting oscillation models, that is square-wave burster. One of the interesting features of these models is that periodic bursting solution need not to be unique or stable for arbitrarily small values of a singular perturbation parameter <TEX>$\epsilon$</TEX>. Recent results show that the bursting solution is uniquely determined and stable for most of the ranges of the small parameter <TEX>$\epsilon$</TEX>. In this paper, we present a condition of uniqueness and stability of periodic bursting solutions for all sufficiently small values of <TEX>$\epsilon$</TEX> > 0.

keywords
bursting, stability, uniqueness

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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