Bifurcation structure of traveling pulses in Type-I excitable media

Moreno-Spiegelberg, Pablo; Arinyo-i-Prats, Andreu; Ruiz-Reynés, Daniel; Matias, Manuel A.; Gomila, Damià
Physical Review E 106, 034206 (1-15) (2022)

We have studied the existence of traveling pulses in a general Type-I excitable 1-dimensional
medium. We have obtained the stability region and characterized the different bifurcations behind
either the destruction or loss of stability of the pulses. In particular, some of the bifurcations
delimiting the stability region have been connected, using singular limits, with the two different
scenarios that mediated the Type-I local excitability, i.e. homoclinic (saddle-loop) and Saddle-Node
on the Invariant Circle bifurcations. The existence of the traveling pulses has been linked, outside
the stability region, to a drift pitchfork instability of localized steady structures.

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