Computation of the topological entropy in chaotic biophysical bursting models for excitable cells
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 mo...
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| Format: | Article |
| Language: | English |
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Wiley
2006-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/DDNS/2006/60918 |
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| _version_ | 1832568051289030656 |
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| author | Jorge Duarte Luís Silva J. Sousa Ramos |
| author_facet | Jorge Duarte Luís Silva J. Sousa Ramos |
| author_sort | Jorge Duarte |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-06526a37a2304cc89addc199d8b10a5d |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-06526a37a2304cc89addc199d8b10a5d2025-02-03T00:59:47ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2006-01-01200610.1155/DDNS/2006/6091860918Computation of the topological entropy in chaotic biophysical bursting models for excitable cellsJorge Duarte0Luís Silva1J. Sousa Ramos2Departmento de Engenharia Química, Secção de Matemática, Instituto Superior de Engenharia de Lisboa, Rua Conselheiro Emídio Navarro 1, Lisboa 1949-014, PortugalDepartmento de Matemática, Universidade de Évora, Évora 7000-671, PortugalDepartmento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais 1, Lisboa 1049-001, PortugalOne 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.http://dx.doi.org/10.1155/DDNS/2006/60918 |
| spellingShingle | Jorge Duarte Luís Silva J. Sousa Ramos Computation of the topological entropy in chaotic biophysical bursting models for excitable cells Discrete Dynamics in Nature and Society |
| title | Computation of the topological entropy in chaotic biophysical bursting models for excitable cells |
| title_full | Computation of the topological entropy in chaotic biophysical bursting models for excitable cells |
| title_fullStr | Computation of the topological entropy in chaotic biophysical bursting models for excitable cells |
| title_full_unstemmed | Computation of the topological entropy in chaotic biophysical bursting models for excitable cells |
| title_short | Computation of the topological entropy in chaotic biophysical bursting models for excitable cells |
| title_sort | computation of the topological entropy in chaotic biophysical bursting models for excitable cells |
| url | http://dx.doi.org/10.1155/DDNS/2006/60918 |
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