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Bezruchko B. P., Prokhorov M. D., Seleznev E. P. Oscillation types, multistability, and basins of attractors in symmetrically coupled period-doubling systems. Izvestiya VUZ. Applied Nonlinear Dynamics, 2002, vol. 10, iss. 4, pp. 47-68. DOI: 10.18500/0869-6632-2002-10-4-47-68

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Oscillation types, multistability, and basins of attractors in symmetrically coupled period-doubling systems

Bezruchko Boris Petrovich, Saratov State University
Prokhorov Mihail Dmitrievich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Seleznev Evgeny Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences

Symmetrically coupled nonlinear oscillator systems demonstrating transition to chaos via a sequence of period-doubling bifurcations under the control parameter variation exhibit various types of mutual synchronization. For these coupled systems, with dissipatively coupled logistic maps, we consider a hierarchy of possible oscillation types using the magnitude оf the time shift between subsystem oscillations аs а basis for multistable states classification. For oscillation states and their basins of attraction the ways of evolution are studied under nonlinearity and coupling variation. Obtained results are compared with those of physical experiment with a system of coupled, periodically driven nonlinear resonators.

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The work was carried out with the support of the Russian Foundation for Basic Research, grant No. 02-02-17578, state contract No. of the Ministry of Industry and Science of the Russian Federation and CRDF, REC-006.
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