Chaotic oscillations and noise transformations in a simple dissipative system with delayed feedback |
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Authors: | V V Zverev B Ya Rubinstein |
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Institution: | (1) Department of Higher Mathematics, Ural Polytechnical Institute, 620002 Sverdlovsk K-2, USSR;(2) Institute of Metal Physics, 620219 Sverdlovsk GSP-170, USSR |
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Abstract: | We analyze the statistical behavior of signals in nonlinear circuits with delayed feedback in the presence of external Markovian noise. For the special class of circuits with intense phase mixing we develop an approach for the computation of the probability distributions and multitime correlation functions based on the random phase approximation. Both Gaussian and Kubo-Andersen models of external noise statistics are analyzed and the existence of the stationary (asymptotic) random process in the long-time limit is shown. We demonstrate that a nonlinear system with chaotic behavior becomes a noise amplifier with specific statistical transformation properties. |
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Keywords: | Dynamical systems Markov process delayed feedback probability distributions Lyapunov exponent |
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