Entrainment by Chaos

AKHMET M., Fen M. O.

JOURNAL OF NONLINEAR SCIENCE, vol.24, no.3, pp.411-439, 2014 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 24 Issue: 3
  • Publication Date: 2014
  • Doi Number: 10.1007/s00332-014-9194-9
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.411-439
  • Keywords: Limit cycle, Sensitivity, Period-doubling cascade, Hopf bifurcation, Toroidal attractor, Chua's oscillator, Chaos control, GENERALIZED SYNCHRONIZATION, HOPF-BIFURCATION, DYNAMICAL SYNTHESIS, DUFFING EQUATION, SYSTEMS, BEHAVIOR, MODEL, OSCILLATORS, STABILITY, ROUTES
  • TED University Affiliated: No


A new phenomenon, the entrainment of limit cycles by chaos, which results from the appearance of cyclic irregular behavior, is discussed. In this study, sensitivity is considered as the main ingredient of chaos to be captured, and the period-doubling cascade is chosen for extension. Theoretical results are supported by simulations and discussions regarding Chua's oscillators, entrainment of toroidal attractors by chaos, synchronization, and controlling problems. It is demonstrated that the entrainment cannot be considered as generalized synchronization of chaotic systems.