Complex regimes of synchronization

by Azamat Yeldesbay

Institution: Universität Potsdam
Degree: PhD
Year: 2015
Record ID: 1107397
Full text PDF: https://publishup.uni-potsdam.de/opus4-ubp/frontdoor/index/index/docId/7334


Synchronization is a fundamental phenomenon in nature. It can be considered as a general property of self-sustained oscillators to adjust their rhythm in the presence of an interaction. In this work we investigate complex regimes of synchronization phenomena by means of theoretical analysis, numerical modeling, as well as practical analysis of experimental data. As a subject of our investigation we consider chimera state, where due to spontaneous symmetry-breaking of an initially homogeneous oscillators lattice split the system into two parts with different dynamics. Chimera state as a new synchronization phenomenon was first found in non-locally coupled oscillators system, and has attracted a lot of attention in the last decade. However, the recent studies indicate that this state is also possible in globally coupled systems. In the first part of this work, we show under which conditions the chimera-like state appears in a system of globally coupled identical oscillators with intrinsic delayed feedback. The results of the research explain how initially monostable oscillators became effectivly bistable in the presence of the coupling and create a mean field that sustain the coexistence of synchronized and desynchronized states. Also we discuss other examples, where chimera-like state appears due to frequency dependence of the phase shift in the bistable system. In the second part, we make further investigation of this topic by modeling influence of an external periodic force to an oscillator with intrinsic delayed feedback. We made stability analysis of the synchronized state and constructed Arnold tongues. The results explain formation of the chimera-like state and hysteric behavior of the synchronization area. Also, we consider two sets of parameters of the oscillator with symmetric and asymmetric Arnold tongues, that correspond to mono- and bi-stable regimes of the oscillator. In the third part, we demonstrate the results of the work, which was done in collaboration with our colleagues from Psychology Department of University of Potsdam. The project aimed to study the effect of the cardiac rhythm on human perception of time using synchronization analysis. From our part, we made a statistical analysis of the data obtained from the conducted experiment on free time interval reproduction task. We examined how ones heartbeat influences the time perception and searched for possible phase synchronization between heartbeat cycles and time reproduction responses. The findings support the prediction that cardiac cycles can serve as input signals, and is used for reproduction of time intervals in the range of several seconds. Synchronisation ist ein fundamentales Naturphänomen. Es ist die grundlegende Eigenschaft sich selbsterhaltender Oszillatoren, in Gegenwart einer Wechselwirkung, danach zu streben, ihre Rhythmen anzupassen. In dieser Arbeit betrachten wir komplexe Synchronisationszustände sowohl mit Hilfe analytischer Methoden als auch durch numerische Simulation und in experimentellen Daten. …