Discrete Dynamics in Nature and Society
Volume 2006 (2006), Article ID 60918, 18 pages
doi:10.1155/DDNS/2006/60918
Computation of the topological entropy in chaotic biophysical bursting models for excitable cells
1Departmento de Engenharia Química, Secção
de Matemática, Instituto Superior de Engenharia de Lisboa, Rua Conselheiro Emídio Navarro 1, Lisboa 1949-014, Portugal
2Departmento de Matemática, Universidade de Évora, Évora 7000-671, Portugal
3Departmento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais 1, Lisboa 1049-001, Portugal
Received 16 September 2005; Accepted 19 December 2005
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.
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.