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Zulpukarov M. M., Malinetskii G. G., Podlazov A. V. Bifurcation theory inverse problem in a noisy dynamical system. Example solution. Izvestiya VUZ. Applied Nonlinear Dynamics, 2005, vol. 13, iss. 6, pp. 3-23. DOI: 10.18500/0869-6632-2005-13-5-3-23

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Bifurcation theory inverse problem in a noisy dynamical system. Example solution

Zulpukarov Magomed-Gerej Medzhidovich, Keldysh Institute of Applied Mathematics (Russian Academy of Sciences)
Malinetskii Georgij Gennadevich, Keldysh Institute of Applied Mathematics (Russian Academy of Sciences)
Podlazov Andrej Viktorovich, Keldysh Institute of Applied Mathematics (Russian Academy of Sciences)

Bifurcations in nonlinear systems with weak noise are considered. The local bifurcations are discussed: the saddle-node bifurcation, the transcritical bifurcation, the supercritical and subcritical pitchfork bifurcations. Basing on the known prebifurcational noise rise and saturation phenomenon, the inverse problem is introduced: the problem of the bifurcation detection and determining it’s type by the observed noise change (noise deviation growth fashion, saturation level, probability density). The inverse problem solution algorithm is suggested.

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