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

quasi-periodic bifurcations

«Oscillator death» and quasiperiodic bifurcations in low-dimensional ensemble of van der Pol oscillators

The dynamics of the four dissipatively coupled van der Pol oscillator is considered. Lyapunov chart is presented in the parameter plane and its arrangement is discusses. The effect of increase of the threshold for the «oscillator death» regime and the possibility of complete and partial broadband synchronization are revealed. We discuss the bifurcations of tori in the system at large frequency detuning of the oscillators, in particular, quasiperiodic saddle-node and Hopf bifurcations.

Maps with quasi-periodicity of different dimension and quasi-periodic bifurcations

The paper discusses the construction of convenient and informative three-dimensional mappings demonstrating the existence of 2-tori and 3-tori. The first mapping is obtained by discretizing the continuous time system – a generator of quasi-periodic oscillations. The second is obtained via discretization of the Lorentz-84 climate model. The third mapping was proposed in the theory of quasi-periodic bifurcations by Simo, Broer, Vitolo.