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Information × Registration Number 0214U005205, 0111U006118 , R & D reports Title Investigation of dynamics of nonlinear oscillators and their time series popup.stage_title Head Ihor A. Knyaz, Registration Date 13-03-2014 Organization Sumy State University popup.description2 The questions of self-synchronization in a system of weak-nonlinear oscillators with feedback on example of two self-sustained oscillation systems are discussed. It is shown that synchronization occurs in a narrow domain of values of coupling parameter; outside of this domain the dynamic of the system is autonomous. It is shown that the breaking of synchronization regime is due to change of topology of attractor which is phase incoherent. A nontrivial phenomenon in stochastic zero-dimensional systems, namely, the symmetry breakdown of stationary probability function due to the correlation between the noises is studied. In the frameworks of theoretical approximation and numerical simulations it is shown the fluctuation cross-correlations break the symmetry of bistable synergetic potential, producing an asymmetric effective potential. At that, cross-correlations play the twofold role: cross-correlations are the reason of symmetry breaking at small cross-correlation times on the one hand, and the reason of symmetry restoring at large values of cross-correlation times on the other hand. Moreover, it is shown that symmetry breakdown occurs only if one of multiplicative function is odd. In the paper we analytically describe the formation of photocount statistics of nonpolarized Gaussian optical radiation when there is a statistical link between the modes of polarization. Analytical expression for the generating function of photocounts was obtained. It was calculated the distributions of a set of probability amplitudes for the cases of correlated and uncorrelated modes. It was shown the statistical relationship between the modes of polarization leads to a broadening of the whole distribution of photocounts with the unchanged first moment. Product Description popup.authors popup.nrat_date 2020-04-02 Close