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Reduction of a model of an excitable cell to a one-dimensional map
Journal article   Peer reviewed

Reduction of a model of an excitable cell to a one-dimensional map

Georgi S. Medvedev
Physica. D, v 202(1), pp 37-59
2005

Abstract

Neurons One-dimensional map Singularly perturbed systems
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.

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Web of Science research areas
Mathematics, Applied
Physics, Fluids & Plasmas
Physics, Mathematical
Physics, Multidisciplinary
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