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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2005; 42(4): 827-845

Printed July 1, 2005

Copyright © The Korean Mathematical Society.

Stability analysis of bursting models

Euiwoo Lee

Soongsil University

Abstract

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In this paper, we present a general method for the stability analysis of some bursting models. Our method is geometric in the sense that we consider a flow-defined return map defined on a section and determine when the map is a contraction. We find that there are three different stability types in the codimension-1 planar bursters.

Keywords: bursting, stability, bifurcation, delayed behavior, singular perturbation

MSC numbers: 34D15, 34C23, 92B05

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