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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.
We characterise the evolution of a dynamical system by combining two well-known complex systems tools, namely, symbolic ordinal analysis and networks. From the ordinal representation of a time-series we construct a network in which every node weights
Let $G$ be the group $mathbb{Z}^d$ or the monoid $mathbb{N}^d$ where $d$ is a positive integer. Let $X$ be a subshift over $G$, i.e., a closed and shift-invariant subset of $A^G$ where $A$ is a finite alphabet. We prove that the topological entropy o
Symbolic sequences with long-range correlations are expected to result in a slow regression to a steady state of entropy increase. However, we prove that also in this case a fast transition to a constant rate of entropy increase can be obtained, prov
We present a simple method to efficiently compute a lower limit of the topological entropy and its spatial distribution for two-dimensional mappings. These mappings could represent either two-dimensional time-periodic fluid flows or three-dimensional
Harnessing chaos or intrinsic nonlinear behaviours from dynamical systems is a promising avenue for the development of unconventional information processing technologies. However, the exploitation of such features in spintronic devices has not been a