Recurrence analysis and synchronization of oscillators with coexisting attractors

The method of recurrence plots (RPs) has been traditionally used for experimental time series analysis with no comparison with the mathematical model. This is in part because of lack of nonlinear analysis of mathematical model based on the recurrence quantification analysis (RQA) parameters. The paper provides substantial information about the mathematical and numerical analysis and synchronization of a multi-limit cycle oscillator from the RQA perspective. The recurrence quantification analysis parameters are used to discuss the birhythmic behavior of the system, as well as various bifurcations (quasi-periodicity, periodicity and chaos) in the system response. Finally, the results of the method of RPs are compared to those of phase diagrams and the problem of synchronization of limit cycle and chaotic response is discussed by the mean of cross recurrence.