For citation:
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
Relaxation of probability characteristics of dynamical systems, described by Ferhulst stochastic equation with «pink» noise
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.
- Dimentberg MF. Nonlinear stochastic problems of mechanical oscillations. М.: Nauka; 1980. 368 p. (in Russian).
- Moss B, McClintock PVE, editors. Noise in Nonlinear Dynamical Systems. Vol. 1: Theory of Continuous Fokker-Planck Systems. Vol. 2: Theory of Noise Induced Processes in Special Applications. Vol. 3: Experiments and Stimulations. England, Cambridge: Cambridge Univercity Press; 1989. 352 p, 388 p, 278 p.
- Horsthemke W, Lefever R. Noise-Induced Transitions: Theory and Applications in Physics, Chemistry, and Biology. Berlin: Springer; 1987. 322 p.
- Feller W. An Introduction to Probability Theory and Its Applications. Vol. 1, 2. New York: Wiley; 1968. 509 p, 704 p.
- Klyatskin VI. Stochastic equations and waves in randomly heterogeneous media. M.: Nauka; 1980. 336 p. (in Russian).
- Malakhov AN. Cumulative analysis of non-Gaussian random processes and their transformations. М.: Sovetskoye Radio; 1978. 376 p. (in Russian).
- Dimentberg MF. Exact solutions of the fokker—planck— kolmogorov equation for certain multidimensional dynamic systems. Journal of Applied Mathematics and Mechanics. 1983;47(4):458-460. DOI: 10.1016/0021-8928(83)90082-5.
- Musychuk OV. Some accurate results for the probabilistic characteristics of the stochastic Verhulst equation. Izvestiya VUZ. Applied Nonlinear Dynamics. 1996;4(3):18. (in Russian).
- Musychuk OV. Analytical-numerical construction of probability distributions for one class of nonlinear stochastic systems. Radiophysics and Quantum Electronics. 2000;43(9):827-834.
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