Journal article
Reduction of a model of an excitable cell to a one-dimensional map
Physica. D, v 202(1), pp 37-59
2005
Abstract
We use qualitative methods for singularly perturbed systems of differential equations and the principle of averaging to compute the first return map for the dynamics of a slow variable (calcium concentration) in the model of an excitable cell. The bifurcation structure of the system with continuous time endows the map with distinct features: it is a unimodal map with a boundary layer corresponding to the homoclinic bifurcation in the original model. This structure accounts for different periodic and aperiodic regimes and transitions between them. All parameters in the discrete system have biophysical meaning, which allows for precise interpretation of various dynamical patterns. Our results provide analytical explanation for the numerical studies reported previously.
Metrics
Details
- Title
- Reduction of a model of an excitable cell to a one-dimensional map
- Creators
- Georgi S. Medvedev - Drexel University
- Publication Details
- Physica. D, v 202(1), pp 37-59
- Publisher
- Elsevier
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000228381200003
- Scopus ID
- 2-s2.0-14944346854
- Other Identifier
- 991019170606104721
InCites Highlights
Data related to this publication, from InCites Benchmarking & Analytics tool:
- Web of Science research areas
- Mathematics, Applied
- Physics, Fluids & Plasmas
- Physics, Mathematical
- Physics, Multidisciplinary