This article is cited in 6 papers

Analytical modeling of processes in dynamical systems with cylindric Bessel nonlinearities

I. N. Sinitsyn

Institute of Informatics Problems, Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation

Abstract: Methods of analytical modeling (MAM) for processes in dynamical systems with complex Bessel nonlinearities with harmonically and stochastically wide and narrow band disturbances are given. Neccessary elements of the cylindric Bessel functions theory and complex Bessel nonlinearities are presented. Methodological and algorithmical support for MAM based on the statistical linearization method (SLM) and the normal approximation method for wide-band stochastic processes (white noise) is developed. Pecularities of MAM for harmonical and narrow band stochastic processes are discussed. Test examples of one-dimensional systems with additive and multiplicative noises and Bessel nonlinearities and for Bessel oscillator with various disturbances are given. Conclusions and some generalizations are mentioned.

Keywords: Bessel nonliearity; Bessel oscillator; complex Bessel nonlinearity; Gibbs formula; harmonical process; Kummer function; method of analytical modeling; narrow band stochastic processes; normal approximation method (NAM); statistical linearization method (SLM); stochastic system on manifold (MStS); white noise; wide band stochastic process.

Received: 13.08.2015

DOI: 10.14357/19922264150404

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