Discrete Dynamics in Nature and Society
Volume 2006 (2006), Article ID 60918, 18 pages

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

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

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.


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.