Synchronization in periodically driven and coupled stochastic systems [Elektronische Ressource] : a discrete state approach / von Tobias Prager

Synchronization in Periodically Driven andCoupled Stochastic Systems–A Discrete StateApproachDISSERTATIONzur Erlangung des akademischen Gradesdoctor rerum naturalium(Dr. rer. nat.)im Fach Physikeingereicht an derMathematisch-Naturwissenschaftlichen Fakultät Ider Humboldt-Universität zu BerlinvonHerrn Dipl. Phys. Tobias Pragergeboren am 30.03.1974 in TübingenPräsident der Humboldt-Universität zu Berlin:Prof. Dr. Christoph MarkschiesDekan der Mathematisch-Naturwissenschaftlichen Fakultät I:Prof. Thomas Buckhout, PhDGutachter:1. Prof. Dr. Lutz Schimansky-Geier2. Prof. Dr. Igor Sokolov3. Prof. Dr. Eckehard Schöll, PhDeingereicht am: 11.01.2006Tag der mündlichen Prüfung: 23.03.2006AbstractWe investigate the behavior of stochastic bistable and excitable dynamics basedon a discrete state modeling. In addition to the well known Markovian two statemodel for bistable dynamics we introduce a non Markovian three state modelfor excitable systems. Its relative simplicity compared to stochastic models ofexcitable dynamics with continuous phase space allows to obtain analytical resultsin different contexts.First, we study the joint influence of periodic signals and noise, both basedon a characterization in terms of spectral quantities and in terms of synchroniza-tion properties with the driving signal. We present expressions for the spectralpower amplification and signal to noise ratio for renewal processes driven by weakperiodic signals.