Dresden 2003 – scientific programme
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DY: Dynamik und Statistische Physik
DY 42: Synchronisation I
DY 42.4: Talk
Thursday, March 27, 2003, 11:45–12:00, G\"OR/226
Synchronization of coupled discrete state oscillators — •Tobias Prager1, Björn Naundorf2, and Lutz Schimansky-Geier1 — 1Theorie Stochastischer Prozesse, Humboldt Universität, Berlin — 2Max-Planck-Institut für Strömungsforschung and Institut für Nichtlineare Dynamik der Universität Göttingen
Collective behaviour and synchronization is a phenomenon which is observed in a variety of different physical, biological and sociological systems consisting of coupled stochastic functional units. To understand the principles of synchronization in these kind of systems we model the constituting parts by stochastic discrete state oscillators. When coupled globally the whole system shows collective oscillations in a large parameter region while the behaviour of a single oscillator remains stochastic. To explain this effect we derive a system of equations for the dynamics of the occupation probabilities and show that the collective oscillations are due to a Hopf-Bifurcation. For a regular topology with few connections between the single oscillators, islands of coherent oscillations are formed. Increasing topological disorder in the framework of small world networks these islands merge. We examine this transition in terms of typical network quantities.