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Register a new userDetecting synchronization of self-sustained oscillators by external driving with varying frequency
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Added by
Alexander E. Hramov
Publication date
2006
fields
Physics
and research's language is
English
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We propose a method for detecting the presence of synchronization of self-sustained oscillator by external driving with linearly varying frequency. The method is based on a continuous wavelet transform of the signals of self-sustained oscillator and external force and allows one to distinguish the case of true synchronization from the case of spurious synchronization caused by linear mixing of the signals. We apply the method to driven van der Pol oscillator and to experimental data of human heart rate variability and respiration.
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In this paper we present an experimental setup and an associated mathematical model to study the synchronization of two self sustained strongly coupled mechanical oscillators (metronomes). The effects of a small detuning in the internal parameters, namely damping and frequency, have been studied. Our experimental system is a pair of spring wound mechanical metronomes, coupled by placing them on a common base, free to move along a horizontal direction. In our system the mass of the oscillating pendula form a significant fraction of the total mass of the system, leading to strong coupling of the oscillators. We modified the internal mechanism of the spring-wound clockwork slightly, such that the natural frequency and the internal damping could be independently tuned. Stable synchronized and anti-synchronized states were observed as the difference in the parameters was varied. We designed a photodiode array based non-contact, non-magnetic position detection system driven by a microcontroller to record the instantaneous angular displacement of each oscillator and the small linear displacement of the base coupling the two. Our results indicate that such a system can be made to stabilize in both in-phase anti-phase synchronized state by tuning the parameter mismatch. Results from both numerical simulations and experimental observations are in qualitative agreement and are both reported in the present work.
The behavior of two unidirectionally coupled chaotic oscillators near the generalized synchronization onset has been considered. The character of the boundaries of the generalized synchronization regime has been explained by means of the modified system
Complexity of dynamical networks can arise not only from the complexity of the topological structure but also from the time evolution of the topology. In this paper, we study the synchronous motion of coupled maps in time-varying complex networks both analytically and numerically. The temporal variation is rather general and formalized as being driven by a metric dynamical system. Four network models are discussed in detail in which the interconnections between vertices vary through time randomly. These models are 1) i.i.d. sequences of random graphs with fixed wiring probability, 2) groups of graphs with random switches between the individual graphs, 3) graphs with temporary random failures of nodes, and 4) the meet-for-dinner model where the vertices are randomly grouped. We show that the temporal variation and randomness of the connection topology can enhance synchronizability in many cases; however, there are also instances where they reduce synchronizability. In analytical terms, the Hajnal diameter of the coupling matrix sequence is presented as a measure for the synchronizability of the graph topology. In topological terms, the decisive criterion for synchronization of coupled chaotic maps is that the union of the time-varying graphs contains a spanning tree.
Due to time delays in signal transmission and processing, phase lags are inevitable in realistic complex oscillator networks. Conventional wisdom is that phase lags are detrimental to network synchronization. Here we show that judiciously chosen phase lag modulations can result in significantly enhanced network synchronization. We justify our strategy of phase modulation, demonstrate its power in facilitating and enhancing network synchronization with synthetic and empirical network models, and provide an analytic understanding of the underlying mechanism. Our work provides a new approach to synchronization optimization in complex networks, with insights into control of complex nonlinear networks.
A feasible model is introduced that manifests phenomena intrinsic to iterative complex analytic maps (such as the Mandelbrot set and Julia sets). The system is composed of two coupled alternately excited oscillators (or self-sustained oscillators). The idea is based on a turn-by-turn transfer of the excitation from one subsystem to another (S.P.~Kuznetsov, Phys.~Rev.~Lett. bf 95 rm, 2005, 144101) accompanied with appropriate nonlinear transformation of the complex amplitude of the oscillations in the course of the process. Analytic and numerical studies are performed. Special attention is paid to an analysis of the violation of the applicability of the slow amplitude method with the decrease in the ratio of the period of the excitation transfer to the basic period of the oscillations. The main effect is the rotation of the Mandelbrot-like set in the complex parameter plane; one more effect is the destruction of subtle small-scale fractal structure of the set due to the presence of non-analytic terms in the complex amplitude equations.
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