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Small amplitude oscillation in the refractory tail of solitary pulses are shown to have a strong impact on the interaction between excitation pulses. First, annihilation of colliding pulses is replaced by reflective collision. Second, in the same parameter range we find bistability in the dispersion relation for periodic pulse trains [1]. This bistability results in alternative stable pulse trains of same wavelength propagating at a different speed. Close to the Canard explosion in the local dynamics we observe higher order multistability as well as the break-up of the dispersion curve into disconnected branches accompanied by the formation of isolas [2]. Finally, our results shed new light on the still open mechanism of the transition between trigger waves and phase waves which represent basic types of wave activity in reaction-diffusion systems [3]. The behaviour is generic for media with a unique homogeneous steady state that undergoes a supercritical Hopf-bifurcation with Canard explosion due to well separated time scales (so-called type II excitable systems [4]).
[1] G. Bordiougov and H. Engel, Oscillatory Dispersion and Coexisting Stable Pulse Trains in an Excitable Medium, Phys. Rev. Lett. 90(14), 148302 (2003) [2] G. Roeder et al, Bistable dispersion relation in an excitable Fitzhugh-Nagumo model, in preparation [3] G. Bordiougov, H. Engel, From Trigger to Phase Waves and Back Again, submitted in Physica D [4] E. Izhikevich, Neural Excitability, Spiking and Bursting, Int. J. of Bif. and Chaos 10 (2000) 1171-1266 |
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