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Updated: Aug 24, 2025

External Excitation of Neurons Using Electric and Magnetic Fields in One- and Two-dimensional Cultures
Published on: May 7, 2017
Bifurcation structure of traveling pulses in type-I excitable media
Pablo Moreno-Spiegelberg1, Andreu Arinyo-I-Prats2, Daniel Ruiz-Reynés3
1IFISC (CSIC-UIB), Instituto de Física Interdisciplinar y Sistemas Complejos, E-07122 Palma de Mallorca, Spain.
Abstract:
We study the scenario in which traveling pulses emerge in a prototypical type-I one-dimensional excitable medium, which exhibits two different routes to excitable behavior, mediated by a homoclinic (saddle-loop) and a saddle-node on the invariant cycle bifurcations. We characterize the region in parameter space in which traveling pulses are stable together with the different bifurcations behind either their destruction or loss of stability. In particular, some of the bifurcations delimiting the stability region have been connected, using singular limits, with the two different scenarios that mediated type-I local excitability. Finally, the existence of traveling pulses has been linked to a drift pitchfork instability of localized steady structures.
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