Control of coherence in excitable systems by the interplay of noise and time-delay
1 Humboldt-Universität zu Berlin, Institut für Physik, Newtonstr. 15, 12489 Berlin, Germany
2 Institute of Physical Chemistry, National Center for Scientific Research “Demokritos”, 15310 Athens, Greece
3 Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
Revised: 23 December 2010
Published online: 18 February 2011
The control of coherence and spectral properties of noise-induced oscillations by time delayed feedback is studied in a FitzHugh-Nagumo system and analyzed by reduced non-Markovian models. A two-state approach is considered as an abstract simplification of this excitable system. Rest and excited states are characterized by different waiting time distributions. This non-Markovian approach allows one to predict quantitatively the increase of coherence measured by the correlation time, and the modulation of the main frequencies of the stochastic dynamics in dependence on the delay time below Hopf bifurcations. Beyond the Hopf bifurcation, bulk oscillations of an ensemble of excitable two-state rotators emerge in the onset of coherent activation in case of delayed mean field coupling of the ensemble.
© EDP Sciences, Springer-Verlag, 2011