"Excitability of the relaxation oscillations in the FitzHugh-Nagumo system"

will be given by Dr Matthias Wolfrum from the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) in Berlin.

Abstract of the talk:

The classical notion of excitability refers to an equilibrium state that shows under the influence of perturbations a nonlinear threshold-like behavior. In this talk, we extend this concept by demonstrating how periodic orbits can exhibit a specific form of excitable behavior where the nonlinear threshold-like response appears only after perturbations applied within a certain part of the periodic orbit, i.e the excitability happens to be phase-sensitive. We demonstrate this concept using the relaxation oscillations of the FitzHugh-Nagumo system. Triggering the phase-sensitive excitability by noise leads to a characteristic non-monotone dependence of the mean spiking rate of the relaxation oscillations on the noise level. In the second part of the talk, we consider a system of two coupled FitzHugh-Nagumo oscillators, where dynamical regimes with alternating spiking order, called leap-frogging, appear as a consequence of the phase-sensitive excitability feature. We analyze various types of periodic and chaotic leap-frogging regimes, using numerical path-following methods to investigate their emergence and stability, as well as to obtain the complex bifurcation scenario which organizes their appearance in the parameter space.

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