Analytical Solutions For Traveling Pulses And Wave Trains In Neural Models: Excitable And Oscillatory Regimes
ADVANCED MATHEMATICAL METHODS IN BIOSCIENCES AND APPLICATIONS(2019)
摘要
We consider a piecewise linear approximation of the diffusive Morris-Lecar model of neuronal activity, the Tonnelier-Gerstner model. Exact analytical solutions for one-dimensional excitation waves are derived. The dynamics of traveling waves is related to two basic regimes of wave propagation: excitable and oscillatory cases. In the first case we describe mathematically the structure of a solitary pulse and in the second case-the form of a periodic sequence of pulses (a periodic wave train).
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关键词
Reaction-diffusion equations, Piecewise linear models, Traveling waves
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