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Quasi-periodic bifurcations and “amplitude death” in low-dimensional ensemble of van der Pol oscillators |
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| Authors: | YuP Emelianova AP Kuznetsov LV Turukina |
| Institution: | 1. Department of Electronics and Instrumentation, Saratov State Technical University, Polytechnicheskaya 77, Saratov 410054, Russian Federation;2. Kotel?nikov?s Institute of Radio-Engineering and Electronics of RAS, Saratov Branch, Zelyenaya 38, Saratov 410019, Russian Federation;3. Institute for Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24-25, 14476 Potsdam, Germany |
| Abstract: | The dynamics of the four dissipatively coupled van der Pol oscillators is considered. Lyapunov chart is presented in the parameter plane. Its arrangement is discussed. We discuss the bifurcations of tori in the system at large frequency detuning of the oscillators. Here are quasi-periodic saddle-node, Hopf and Neimark–Sacker bifurcations. The effect of increase of the threshold for the “amplitude death” regime and the possibilities of complete and partial broadband synchronization are revealed. |
| Keywords: | Chain of van der Pol oscillators Bifurcations of tori Amplitude death Broadband synchronization |
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