Computation of the topological entropy in chaotic biophysical bursting models for excitable cells
type: Item
instance of: scholarly article
title: Computation of the topological entropy in chaotic biophysical bursting models for excitable cells
zbMATH Open document ID: 1106.92012
DOI: 10.1155/DDNS/2006/60918
author: N. E. Zubov
published in: Discrete Dynamics in Nature and Society
publication date: 2007-03-19T00:00:00Z
full work available at URL: https://eudml.org/doc/126958
review text: Summary: One of the interesting complex behaviors in many cell membranes is bursting, in which a rapid oscillatory state alternates with phases of relative quiescence. Although there is an elegant interpretation of many experimental results in terms of nonlinear dynamical systems, the dynamics of bursting models is not completely described. We study the dynamical behavior of two specific three-variable models from the literature that replicate chaotic bursting. With results from symbolic dynamics, we characterize the topological entropy of one-dimensional maps that describe the salient dynamics of the attractors. The analysis of the variation of this important numerical invariant with the parameters of the systems allows us to quantify the complexity of the phenomenon and to distinguish different chaotic scenarios. This work provides an example of how our understanding of physiological models can be enhanced by the theory of dynamical systems.
Mathematics Subject Classification ID: 92C20
Mathematics Subject Classification ID: 37N25
Mathematics Subject Classification ID: 92C37
Mathematics Subject Classification ID: 37B40
Mathematics Subject Classification ID: 37B10
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 5134620
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5134620