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Quantifying sudden changes in dynamical systems using symbolic networks
Masoller Alonso, Cristina; Hong, Yanhua; Ayad, Sarah; Gustave, Francois; Barland, Stéphane; Pons Rivero, Antonio Javier; Gómez, Sergio; Arenas, Alex
Universitat Politècnica de Catalunya. Departament de Física i Enginyeria Nuclear; Universitat Politècnica de Catalunya. DONLL - Dinàmica no lineal, òptica no lineal i làsers
We characterize 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 weight represents the probability of an ordinal pattern (OP) to appear in the symbolic sequence and each edge's 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.
Peer Reviewed
Àrees temàtiques de la UPC :: Física
Nonlinear systems
Time-series analysis
complex networks
time series analysis
nonlinear dynamical systems
pseudoperiodic time-series
permutation entropy
complex network
statistical complexity
Sistemes no lineals
Sèries temporals -- Anàlisi

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