DEVELOPMENT OF METHODOLOGICAL AND SOFTWARE SUPPORT FOR ANALYTICAL MODELING OF STOCHASTIC SYSTEMS WITH ELLIPTIC NONLINEARITIES
Abstract
Analytical modeling methodological and software support based on methods of normal approximation (MNA) and statistical linearizations (MSL) for stochastic systems (StS) with elliptic nonlinearities (EN) is given. For typical EN described by Jacobi, Weirestrass etc bank of MSL coefficients is presented. Software tools for dynamical StS are designed in MATLAB-MAPLE. Test example is given.
References
2. Sinitsyn I. N. 2015. Analiticheskoe modelirovanie protsessov v dinamicheskikh sistemakh s tsilindricheskimi besselevymi nelineynostyami [Analytical modeling of processes in dynamical systems with cylindric Bessel nonlinearities] // Informatika i ee primeneniya. 9(4). 39-49.
3. Sinitsyn I. N., Korepanov E. R., Belousov V. V. 2016. Simvol'noe analiticheskoe modelirovanie normal'nykh protsessov v stokhasticheskikh sistemakh so slozhnymi besselevymi nelineynostyami drobnogo poryadka [Symbolic Analytical Modeling of Normal Processes in Stochastic Systems with Complex Fraction Order Bessel nonlinearities] // Sistemy i sredstva informatiki. 26(3). 26–47.
4. Sinitsyn I. N. Analiticheskoe modelirovanie normal'nykh protsessov v stokhasticheskikh sistemakh s ellipticheskimi nelineynostyami Yakobi [Analytical modeling of normal processes in stochastic systems with elliptic nonlinearities Jacobi] // Sistemy i sredstva informatiki, 2017. 27( 1). 4–20.
5. Spravochnik po spetsial'nym funktsiyam / Pod red. M. Abramovicha i I. Stigana. - M.: Nauka. 1979. 832 s.
6. Popov B. A., Tesler G. S. 1984. Vychislenie funktsiy na EVM: Spravochnik. - Kiev: Naukova Dumka. 599~s.
7. Pugachev V. S., Sinitsyn I. N. 1987. Stokhasticheskie differentsial'nye sistemy. Analiz i fil'tratsiya. – M.: Nauka, 1990. 632 s. [Angl. per. Stochastic Differential Systems. Analysis and Filtering. – Chichester, New York: Jonh Wiley. 549 p.].
8. Pugachev V. S., Sinitsyn I. N. } 2000; 2004. Teoriya stokhasticheskikh sistem. – M.: Logos. 1000 s. [Angl. per. Stochastic Systems. Theory and Applications. – Singapore: World Scientific, 2001. 908 p.].
9. Sinitsyn I. N., Sinitsyn V. I. 2013. Lektsii po normal'noy i ellipsoidal'noy approksimatsii raspredeleniy v stokhasticheskikh sistemakh [Lectures on Normal and Ellipsoidal Approximation in Stochastic Systems]. – M.: Torus Press. 488 s.
10. Sinitsyn I. N., Sinitsyn V. I., Korepanov E. R. 2015.Modelirovanie normal'nykh protsessov v stokhasticheskikh sistemakh so slozhnymi transtsendentnymi nelineynostyami // Informatika i ee primeneniya. 9(2). 23–29.
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