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Nonlinear Dynamics

, Volume 86, Issue 1, pp 227–234 | Cite as

Measuring phase synchronization in periodically driven Lü oscillator with a phase-incoherent attractor

  • Yao-Chen Hung
  • Tzu-Fang Hsu
Original Paper

Abstract

A signal-based synchronization coefficient is proposed to quantify phase synchronization in the periodically driven Lü system, which is a phase-incoherent chaotic system. Phase synchronization is verified in advance using some traditional methods, and the relevant results are compared with those obtained using the proposed synchronization coefficient. The coefficient is determined by a series of scenarios, which are signal decomposition based on empirical mode decomposition, phase transformation based on the Hilbert transform, and degree quantification based on Shannon entropy. The route to phase synchronization is demonstrated to be well characterized without prior knowledge of the formulation or the attractor structure of Lü system.

Keywords

Phase synchronization Phase-incoherent attractor Chaotic system 

Notes

Acknowledgments

We thank Dr. Ming-Chya Wu for helpful discussions on the EMD method.

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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Physics Teaching and Research CenterFeng Chia UniversityTaichungTaiwan
  2. 2.Department of Applied PhysicsNational Pingtung UniversityPingtungTaiwan

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