Velocity of pulses in discrete excitable systems

The pulse solution of the spatially discrete excitable FitzHugh–Nagumo (FHN) system is approximately constructed using matched asymptotic expansions in the limit of large time scale separation (as measured by a small dimensionless parameter ϵ). The pulse profile typically consists of slowly varying...

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Bibliographic Details
Published in:Nonlinear analysis: real world applications 2012-12, Vol.13 (6), p.2794-2803
Main Authors: Arana, J.I., Bonilla, L.L.
Format: Article
Language:English
Subjects:
Approximation
Asymptotic expansions
Dimensional measurements
Discrete FitzHugh–Nagumo system
Excitable systems
Excitation
Matched asymptotic expansions
Mathematical analysis
Mathematical models
Nonlinear pulses and wave fronts
Nonlinearity
Wave fronts
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Summary:The pulse solution of the spatially discrete excitable FitzHugh–Nagumo (FHN) system is approximately constructed using matched asymptotic expansions in the limit of large time scale separation (as measured by a small dimensionless parameter ϵ). The pulse profile typically consists of slowly varying regions of the excitatory variable separated by sharp wave fronts. In the FHN system, the velocity of a pulse is decided by the interaction between its leading and trailing fronts, but the leading order approximation gives only a fair result when compared with direct numerical solutions. A higher order approximation to the wave fronts comprising the FHN pulse is found. Our approximation provides an ϵ-dependent pulse velocity that approximates much better the velocity obtained from numerical solutions. As a result, the reconstruction of the FHN pulse using the improved wave fronts is much closer to the numerically obtained pulse.
ISSN:1468-1218
1878-5719
DOI:10.1016/j.nonrwa.2012.03.016