ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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Muzychuk O. V. Relaxation of probability characteristics of dynamical systems, described by Ferhulst stochastic equation with «pink» noise. Izvestiya VUZ. Applied Nonlinear Dynamics, 2000, vol. 8, iss. 5, pp. 36-42. DOI: 10.18500/0869-6632-2000-8-5-36-42

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Relaxation of probability characteristics of dynamical systems, described by Ferhulst stochastic equation with «pink» noise

Muzychuk Oleg Vladimirovich, Nizhny Novgorod State University of Architecture

Probability characteristics relaxation of а solution of Ferhulst stochastic equation is considered. It was supposed, that random influence on the system is Gaussian Markov process with arbitrary values of correlation time. Two models of nonstationary probability distributions with exact stationary athymptotic are proposed on the basis of numerical solutions of relaxation equations for moments: in the case of delta—correlated random force and quasistationary force. Relaxation of main probability characteristics is examined in dependence оп nonlinearity, initial conditions, noise intensity and kind of noise spectrum. Evolution of the model probability distributions has been constructed.

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The work was supported by the RFBR, project № 99-02-17544 and № 00-15-96620.
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