Michael Rosenblum

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We use the concept of phase synchronization for the analysis of noisy nonstationary bivariate data. Phase synchronization is understood in a statistical sense as an existence of preferred values of the phase di erence, and two techniques are proposed for a reliable detection of synchronous epochs. These methods are applied to magnetoencephalograms and(More)
We present the new effect of phase synchronization of weakly coupled self-sustained chaotic oscillators. To characterize this phenomenon, we use the analytic signal approach based on the Hilbert transform and partial Poincaré maps. For coupled Rössler attractors, in the synchronous regime the phases are locked, while the amplitudes vary chaotically and are(More)
There is evidence that physiological signals under healthy conditions may have a fractal temporal structure. Here we investigate the possibility that time series generated by certain physiological control systems may be members of a special class of complex processes, termed multifractal, which require a large number of exponents to characterize their(More)
Synchronization of coupled oscillating systems means appearance of certain relations between their phases and frequencies. Here we use this concept in order to address the inverse problem and to reveal interaction between systems from experimental data. We discuss how the phases and frequencies can be estimated from time series and present techniques for(More)
We propose a method for experimental detection of directionality of weak coupling between two self-sustained oscillators from bivariate data. The technique is applicable to both noisy and chaotic systems that can be nonidentical or even structurally different. We introduce an index that quantifies the asymmetry in coupling.
shape, scaled so that R(K)=1, with total length L. The inverse-square ‘energy’ (S(K), A, writhe, and so on) can be estimated by assuming the ‘mass’ of the knot is concentrated at points p on the integer lattice. Concentric shells of unit thickness about each p each contribute the same amount, so the contribution for p is that constant multiplied by the(More)
We investigate synchronization between cardiovascular and respiratory systems in healthy humans under free-running conditions. For this aim we analyze nonstationary irregular bivariate data, namely, electrocardiograms and measurements of respiratory flow. We briefly discuss a statistical approach to synchronization in noisy and chaotic systems and(More)
We study synchronization transitions in a system of two coupled self-sustained chaotic oscillators. We demonstrate that with the increase of coupling strength the system first undergoes the transition to phase synchronization. With a further increase of coupling, a new synchronous regime is observed, where the states of two oscillators are nearly identical,(More)
We consider the problem of experimental detection of directionality of weak coupling between two self-sustained oscillators from bivariate data. We further develop the method introduced by Rosenblum and Pikovsky [Phys. Rev. E 64, 045202 (2001)], suggesting an alternative approach. Next, we consider another framework for identification of directionality,(More)
Biological time-series analysis is used to identify hidden dynamical patterns which could yield important insights into underlying physiological mechanisms. Such analysis is complicated by the fact that biological signals are typically both highly irregular and non-stationary, that is, their statistical character changes slowly or intermittently as a result(More)