Quantifying sudden changes in dynamical systems using symbolic networks

Abstract

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 represents the probability of an ordinal patterns (OPs) to appear in the symbolic sequence and each edges weight represents the probability of transitions between two consecutive OPs. Several network-based diagnostics are then proposed to characterize the dynamics of different systems: logistic, tent and circle maps. We show that these diagnostics are able to capture changes produced in the dynamics as a control parameter is varied. We also apply our new measures to empirical data from semiconductor lasers and show that they are able to anticipate the polarization switchings, thus providing early warning signals of abrupt transitions.

18 pages, 9 figures, to appear in New Journal of Physics

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• Unveiling the connectivity of complex networks using ordinal transition methods
• Identifying and anticipating the threshold bifurcation of a complex laser with permutation entropy
• Using symbolic networks to analyse dynamical properties of disease outbreaks
• Symbolic dynamics of joint brain states during dyadic coordination