Predicting phase synchronization of nonphase-coherent chaos

¹  School of Information Science, Japan Advanced Institute of Science and Technology - Ishikawa 923-1292, Japan
²  Department of Physics, Humboldt University Berlin - Newtonstr. 15, 12489 Berlin, Germany
³  Potsdam Institute for Climate Impact Research - Telegraphenberg A 31, 14473 Potsdam, Germany
⁴  Department of Chemistry, Saint Louis University - 3501 Laclede Ave., St. Louis, MO 63103-2010, USA
⁵  Department of Chemical Engineering, University of Virginia - 102 Engineers' Way, Charlottesville, VA 22904, USA

Corresponding author: isao@jaist.ac.jp

Received: 18 January 2008
Accepted: 8 July 2008

Abstract

A new approach is presented for the reconstruction of phase synchronization phenomena from measurement data of two coupled chaotic oscillators. The oscillators are assumed to be nonphase-coherent, making the synchronization analysis extremely difficult. To deal with such nonphase-coherent systems, a CPR index has been recently developed based on the idea of recurrence plot. The present study combines a nonlinear modeling technique with the CPR index to recover the synchronization diagram of nonphase-coherent oscillators. Lyapunov exponents are also utilized to locate the onset point of synchronization. This allows the prediction of the regime of phase synchronization as well as non-synchronization in a broad parameter space of coupling strength without further experiments. The efficiency of this technique is demonstrated with simulated data from two coupled Rössler oscillators as well as with experimental data from electrochemical oscillators.