Ensembles of several chaotic R¨ossler oscillators are considered. It is shown that a typical phenomenon for such systems is the emergence of invariant tori of different and sufficiently high dimension. The possibility of a quasi-periodic Hopf bifurcation and of the cascade of such bifurcations based on tori of increasing dimension is demonstrated. The domains of resonant tori are revealed whose boundaries correspond to a saddle-node bifurcation. Within areas of resonant modes the torus-doubling bifurcations and tori destruction are observed.
Keywords:
chaos, quasiperiodic oscillations, invariant tori, Lyapunov exponents, bifurcations
Citation:
Kuznetsov A. P., Shchegoleva N. A., Sataev I. R., Sedova Y. V., Turukina L. V., Dynamics of coupled chaotic oscillators: from chaos to quasiperiodicity, Rus. J. Nonlin. Dyn.,
2014, Vol. 10, No. 4,
pp. 387-405
DOI:10.20537/nd1404001