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The European Physical Journal Special Topics

, Volume 224, Issue 8, pp 1459–1467 | Cite as

Rare and hidden attractors in Van der Pol-Duffing oscillators

  • S. Brezetskyi
  • D. Dudkowski
  • T. Kapitaniak
Review
Part of the following topical collections:
  1. Multistability: Uncovering Hidden Attractors

Abstract

We study the dynamics of the single and coupled van der Pol-Duffing oscillators. Each oscillator is characterized by the multistability (the coexistence of attractors). Some of the coexisting attractors have very small basins of attraction (the rare ones) and some of them do not contain equilibria in their basin of attraction (the hidden ones). We perform the detailed bifurcation analysis of these attractors and investigate how this plethora of states influences the dynamics of the network of coupled oscillators. We have observed the cluster synchronization on different attractors as well as different types of chimera states.

Keywords

European Physical Journal Special Topic Chaotic Attractor Periodic Attractor Poincare Section Cluster Synchronization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© EDP Sciences and Springer 2015

Authors and Affiliations

  1. 1.Division of DynamicsLodz University of TechnologyLodzPoland

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