Rhythm synchronization and chaotic modulation of coupled Van der Pol oscillators in a model for the heartbeat

We investigate a phenomenological model for the heartbeat consisting of two coupled Van der Pol oscillators. The coupling between these nodes can be both unidirectional or bidirectional, and an external driving produced by a pacemaker is also included in this model. In order to warrant a robust operation, it is desirable that both units oscillate in a synchronized way, even though in the presence of external influences or parameter mismatches which are unavoidable in a physiological setting. We study the synchronization properties of such an association with respect to the nature and intensity of coupling. We analyze in particular the (generalized) synchronization of rhythms characterized by a chaotic modulation of the oscillator frequencies. We also investigate the shadowing breakdown of numerically generated chaotic trajectories of the coupled oscillator system via unstable dimension variability in its chaotic invariant set.