ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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Bashkirtseva I. A., Perevalova T. V., Ryashko L. B. Analysis of noise­induced bifurcations for the Hopf system. Izvestiya VUZ. Applied Nonlinear Dynamics, 2010, vol. 18, iss. 1, pp. 37-50. DOI: 10.18500/0869-6632-2010-18-1-37-50

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Language: 
Russian
Heading: 
Bifurcations in Dynamical Systems
Article type: 
Article
UDC: 
531.36
DOI: 
10.18500/0869-6632-2010-18-1-37-50

Analysis of noise­induced bifurcations for the Hopf system

Autors: 
Bashkirtseva Irina Adolfovna, Ural Federal University named after the first President of Russia B.N.Yeltsin
Perevalova Tatjana Vladimirovna, Ural Federal University named after the first President of Russia B.N.Yeltsin
Ryashko Lev Borisovich, Ural Federal University named after the first President of Russia B.N.Yeltsin
Abstract: 

We consider the Hopf system as a classical model of a stiff birth of a cycle. In the presence of parametrical and additive random disturbances, various types of the stochastic attractors are observed. The solution of the corresponding Fokker–Planck–Kolmogorov equation is found. The qualitative changes of the form for stochastic attractors under multiplicative noise are shown. The phenomenon of backward stochastic bifurcations is described in details.

Key words: 
Hopf system
cycles
equilibria
stochastic attractors
backward bifurcations
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Received: 
09.03.2009
Accepted: 
20.05.2009
Published: 
31.03.2010
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