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

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Balanov A. G., Vadivasova T. E., Postnov D. E., Sosnovtseva O. V. Bifurcation of chaotic synchronization in Rossler system with harmonic exitation. Izvestiya VUZ. Applied Nonlinear Dynamics, 1997, vol. 5, iss. 5, pp. 31-43. DOI: 10.18500/0869-6632-1997-5-5-31-43

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Russian
Heading: 
Bifurcations in Dynamical Systems
Article type: 
Article
UDC: 
517.9
DOI: 
10.18500/0869-6632-1997-5-5-31-43

Bifurcation of chaotic synchronization in Rossler system with harmonic exitation

Autors: 
Balanov Aleksandr Gennadevich, Loughborough University
Vadivasova Tatjana Evgenevna, Saratov State University
Postnov Dmitrij Engelevich, Saratov State University
Sosnovtseva Olga Vladimirovna, Danmarks Tekniske Universitet
Abstract: 

Synchronization of chaotic oscillations in nonautonomous Rossler system from the point of view its universality for regular and chaotic regimes is investigated. Comparative analysis of different methods of the boundary of chaotic synchronization diagnostics, namely, the locking of basic frequencies. the stabilisation of difference о instant phases of oscillations, and the levelling of mean time of returning to а secant surface, shows the equivalence of the mentioned approaches for spiral chaos. A set of results from numerical simulation allows us to suggest and substantiate hypothesis that there is a bifurcation of chaotic regime as an analogue of a tangent bifurcation for a limit cycle. Analysing the spectrum of Lyapunov exponents two types of chaos outside synchronization region which differ by number of zero Lyapunov exponents are found.

Key words: 
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Acknowledgments: 
The work was partially financed by a grant from the State Committee for Higher Education of Russia for fundamental natural science (grant 95-0-8.3-66).
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Received: 
25.09.1997
Accepted: 
14.10.1997
Published: 
17.12.1997
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