DYNAMICS OF TWO NONIDENTICAL COUPLED SELF-SUSTAINED SYSTEMS WITH PERIOD DOUBLINGS ON THE EXAMPLE OF R ¨ OSSLER OSCILLATORS
Cite this article as:
Kuznetsov A. P., Paksyutov V. I. DYNAMICS OF TWO NONIDENTICAL COUPLED SELF-SUSTAINED SYSTEMS WITH PERIOD DOUBLINGS ON THE EXAMPLE OF R ¨ OSSLER OSCILLATORS. Izvestiya VUZ. Applied Nonlinear Dynamics, 2006, vol. 14, iss. 2, pp. 3-15. DOI: https://doi.org/10.18500/0869-6632-2006-14-2-3-15
The system of two coupled R¨ ossler oscillators is considered. Detailed investigation is carried out on the plane of parameters which control the period-doubling bifurcations in the subsystems. Dynamical regimes in different points of the control parameter plane are determined using the methods of the bifurcation plot and the highest nonzero Lyapunov exponent plot computation. The synchronization picture of two coupled R¨ ossler oscillators is compared with synchronization pictures of more simple systems: two coupled Van der Pol oscillators and coupled logistic maps. The boundary structure of synchroniza- tion areas is investigated by calculation of the system multiplicators, and the sequence of codimension-two points is found.
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BibTeX
author = {A. P. Kuznetsov and V. I. Paksyutov},
title = {DYNAMICS OF TWO NONIDENTICAL COUPLED SELF-SUSTAINED SYSTEMS WITH PERIOD DOUBLINGS ON THE EXAMPLE OF R ¨ OSSLER OSCILLATORS},
year = {2006},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {14},number = {2},
url = {https://old-andjournal.sgu.ru/en/articles/dynamics-of-two-nonidentical-coupled-self-sustained-systems-with-period-doublings-on-the},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2006-14-2-3-15},pages = {3--15},issn = {0869-6632},
keywords = {-},
abstract = {The system of two coupled R¨ ossler oscillators is considered. Detailed investigation is carried out on the plane of parameters which control the period-doubling bifurcations in the subsystems. Dynamical regimes in different points of the control parameter plane are determined using the methods of the bifurcation plot and the highest nonzero Lyapunov exponent plot computation. The synchronization picture of two coupled R¨ ossler oscillators is compared with synchronization pictures of more simple systems: two coupled Van der Pol oscillators and coupled logistic maps. The boundary structure of synchroniza- tion areas is investigated by calculation of the system multiplicators, and the sequence of codimension-two points is found. }}