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Physica D 189 (2004) 830 Synchronization of two non-scalar-coupled limit-cycle oscillators

Summary: Physica D 189 (2004) 830
Synchronization of two non-scalar-coupled limit-cycle oscillators
M.V. Ivanchenkoa,, G.V. Osipova, V.D. Shalfeeva, J. Kurthsb
a Department of Radiophysics, Nizhny Novgorod University, 23 Gagarin Avenue, 603600 Nizhny Novgorod, Russia
b Institute of Physics, University of Potsdam, 10 Am Neuen Palais, D-14415 Potsdam, Germany
Received 2 July 2003; accepted 25 September 2003
Communicated by Y. Kuramoto
Being one of the fundamental phenomena in nonlinear science, synchronization of oscillations has permanently remained
an object of intensive research. Development of many asymptotic methods and numerical simulations has allowed an under-
standing and explanation of various phenomena of self-synchronization. But even in the classical case of coupled van der
Pol oscillators a full description of all possible dynamical regimes, their mutual transitions and characteristics is still lacking.
We present here a study of the phenomenon of mutual synchronization for two non-scalar-coupled non-identical limit-cycle
oscillators and analyze phase, frequency and amplitude characteristics of synchronization regimes. A series of bifurcation
diagrams that we obtain exhibit various regions of qualitatively different behavior. Among them we find mono-, bi- and mul-
tistability regions, beating and "oscillation death" ones; also a region, where one of the oscillators dominates the other one is
observed. The frequency characteristics that we obtain reveal three qualitatively different types of synchronization: (i) on the
mean frequency (the in-phase synchronization), (ii) with a shift from the mean frequency caused by a conservative coupling
term (the anti-phase synchronization), and (iii) on the frequency of one of the oscillators (when one oscillator dominates
the other).


Source: Aickelin, Uwe - School of Computer Science, University of Nottingham


Collections: Computer Technologies and Information Sciences