Dr Matthias Wolfrum

20. April 2022.

You are cordially invited to the SCL seminar of the Center for the Study of Complex Systems, which will be held on Thursday, 11th October 2018 at 14:00 in the library reading room “Dr. Dragan Popović” of the Institute of Physics Belgrade. The talk entitled

“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. The abstract of the talk is provided below.


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.