The European Physical Journal Special Topics

, Volume 225, Issue 13–14, pp 2635–2643 | Cite as

Nonlinear resonance and synchronization in the ring of unidirectionally coupled Toda oscillators

  • Anton Dvorak
  • Vladimir Astakhov
  • Przemyslaw Perlikowski
  • Tomasz Kapitaniak
Open Access
Regular Article Numerical Continuation in Self-sustained Oscillators
Part of the following topical collections:
  1. Temporal and Spatio-Temporal Dynamic Instabilities: Novel Computational and Experimental Approaches


In the ring of unidirectionally coupled Toda oscillators the nonlinear resonance and the synchronization are investigated. It is shown how the nonlinear resonance affects the structure of the main synchronization region. As a result of nonlinear resonance we observe the coexistence of two stable limit cycles near the resonant frequency, which leads to coexistence of periodic and quasi-periodic regimes within the synchronization region.


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© The Author(s) 2016

Open Access This is an Open Access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  1. 1.Department of Radioelectronics and TelecommunicationsYuri Gagarin State Technical University of SaratovSaratovRussia
  2. 2.Division of Dynamics, Lodz University of TechnologyLodzPoland

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