Symbolic relative entropy in quantifying nonlinear dynamics of equalities-involved heartbeats
Symbolic relative entropy, an efficient nonlinear complexity parameter measuring probabilistic divergences of symbolic sequences, is proposed in our nonlinear dynamics analysis of heart rates considering equal states. Equalities are not rare in discrete heartbeats because of the limits of resolution of signals collection, and more importantly equal states contain underlying important cardiac regulation information which is neglected by some chaotic deterministic parameters and temporal asymmetric measurements. The relative entropy of symbolization associated with equal states has satisfied nonlinear dynamics complexity detections in heartbeats and shows advantages to some nonlinear dynamics parameters without considering equalities. Researches on cardiac activities suggest the highest probabilistic divergence of the healthy young heart rates and highlight the facts that heart diseases and aging reduce the nonlinear dynamical complexity of heart rates.