Informatics and Applications

2015, Volume 9, Issue 4, pp 37-47

ANALYTICAL MODELING OF PROCESSES IN DYNAMICAL SYSTEMS WITH CYLINDRIC BESSEL NONLINEARITIES

  • I. N. Sinitsyn

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.

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