Book chapter
Chapter 5 The topology and organization of unstable periodic orbits in Hodgkin-Huxley models of receptors with subthreshold oscillations
Handbook of Biological Physics
2001
Abstract
This chapter describes a set of equations that has been proposed to model neurons with subthreshold oscillations (1) to show that this model can generate chaotic behavior and (2) to describe how the stretching and squeezing mechanisms operate on the phase space for this model. These stretching and squeezing mechanisms in phase space are described in the chapter in terms of topology. The chapter applies a probe to understand how the flow in the phase space appropriate for neurons with subthreshold oscillations is deformed under the deterministic equations of the model. The chapter shows that the mechanism involved is responsible for chaos in the Duffing oscillator and in the YAG laser. It reviews the basic Hodgkin–Huxley model of electrical activity in a neuron and its modified version. This model describes nerve cells that fire without external inputs. The chapter describes the behavior of the output of this model and the classification of low-dimensional strange attractors by topological means. It outlines the topological analysis program to the analysis of the strange attractors generated by the modified Hodgkin–Huxley equations.
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5 citations in Scopus
Details
- Title
- Chapter 5 The topology and organization of unstable periodic orbits in Hodgkin-Huxley models of receptors with subthreshold oscillations
- Creators
- R. Gilmore - Drexel UniversityX. pei - University of Missouri–St. Louis
- Publication Details
- Handbook of Biological Physics
- Publisher
- Elsevier
- Resource Type
- Book chapter
- Language
- English
- Academic Unit
- [Retired Faculty]
- Scopus ID
- 2-s2.0-77956771999
- Other Identifier
- 991019173549704721