Dynamics between order and chaos revisited
1 Potsdam Institute for Climate Impact Research, Telegraphenberg A 31, 14473 Potsdam, Germany
2 Centre for Dynamics of Complex Systems, University of Potsdam, 14476 Potsdam, Germany
3 Institute of Physics, Humboldt University Berlin, 12489 Berlin, Germany
Revised: 23 December 2010
Published online: 18 February 2011
We show that dynamics between order and chaos, namely strange nonchaotic dynamics can be efficiently studied by means of recurrence properties. Different transitions to this dynamics in coupled Rössler oscillators are revealed by some measures of complexity based on the recurrence time, which is the time needed for a system to recur to a former visited neighborhood. Furthermore, regions of the parameter space where the system is in non-phase, imperfect-phase or phase synchronization are depicted by means of recurrence based indices such as the generalized autocorrelation function and the correlation of probability of recurrence.
© EDP Sciences, Springer-Verlag, 2011