Computation of the topological entropy in chaotic biophysical bursting models for excitable cells

Duarte, Jorge; Silva, Luís; Ramos, J. Sousa

doi:https://doi.org/10.1155/DDNS/2006/60918

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Volume 2006 | Article ID 060918 | https://doi.org/10.1155/DDNS/2006/60918

Computation of the topological entropy in chaotic biophysical bursting models for excitable cells

Jorge Duarte,¹Luís Silva,²and J. Sousa Ramos³

Received16 Sept 2005

Accepted19 Dec 2005

Published19 Jun 2006

Abstract

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. In the present paper, 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 on 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.

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Copyright

Copyright © 2006 Jorge Duarte et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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