Systems and Means of Informatics
2016, Volume 26, Issue 3, pp 26-47
SYMBOLIC ANALYTICAL MODELING OF NORMAL PROCESSES IN STOCHASTIC SYSTEMS WITH COMPLEX FRACTION ORDER BESSEL NONLINEARITIES
- I. N. Sinitsyn
- E. R. Korepanov
- V. V. Belousov
Abstract
Methodological and algorithmical support for analytical modeling of normal (Gaussian) processes in continuous and discrete stochastic systems (StS) with complex fractional order Bessel nonlinearities (spherical, modified spherical, and Airy) is given. The developed StS support is based on the methods of normal approximation and statistical linearization. For complex fractional order, Bessel nonlinearities series and Hermite representations are used. Special attention is paid to symbolic algorithms and software based on modern computer algebra systems (CAS). A short survey of CAS StS application is given. The test example is devoted to noise immunity of Bessel fraction order oscillator in stochastic media.
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[+] About this article
Title
SYMBOLIC ANALYTICAL MODELING OF NORMAL PROCESSES IN STOCHASTIC SYSTEMS WITH COMPLEX FRACTION ORDER BESSEL NONLINEARITIES
Journal
Systems and Means of Informatics
Volume 26, Issue 3, pp 26-47
Cover Date
2016-08-30
DOI
10.14357/08696527160302
Print ISSN
0869-6527
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
Airy nonlinearity; Bessel function of fractional order; Bessel nonlinearity; method of analytical modeling; method of normal approximation; method of statistical linearization; modificated spherical Bessel function; normal (gaussian) process; spherical Bessel function; stochastic process; symbolic analytical modeling
Authors
I. N. Sinitsyn  , E. R. Korepanov ,
and V. V. Belousov
Author Affiliations
Institute of Informatics Problems, Federal Research Center "Computer Science
and Control", Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
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