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## PAPER Quantifying sudden changes in dynamical systems using symbolic networks

### Citations

31 | Complex network from pseudoperiodic time series: Topology versus dynamics. Phys Rev Lett, - Zhang, Small - 2006 |

10 |
Dynamical aspects of interaction networks,”
- Nicolis, Cantu, et al.
- 2005
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Citation Context ...he work, journal citation and DOI. © 2015 IOPPublishing Ltd andDeutsche PhysikalischeGesellschaft Our approach for defining the links as the TP between symbols was originally proposed byNicolis et al =-=[22]-=- and the use of ordinal analysis was proposed by Sun et al [27]; however, in [27] theweights of the linkswere not defined in terms of TPs (as in [22]), but rather, theywere defined as the number of ti... |

10 | Nuño JC. (2008) From time series to complex networks: The visibility graph - Lacasa, Luque, et al. |

8 | Toral R (2010) Description of stochastic and chaotic series using visibility graphs - Lacasa |

8 |
MI (2004) Patterns of link reciprocity in directed networks
- Garlaschelli, Loffredo
(Show Context)
Citation Context ...ully symmetric network ( =w wij ji,∀i j, ) and ac=1 in a fully directed network (either =w 0ij or =w 0ji ∀i j, ). This asymmetry coefficient is closely related to the concept of reciprocity in graphs =-=[38]-=-. We note that to compute thesemeasures, only the nodes and the links that are present in the network are taken into account.While absent nodes and links, corresponding tomissing or forbidden symbols ... |

7 |
Yang H (2008) Complex network-based time series analysis. Physica A 387: 1381–1386
- Yang
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Citation Context ...mputedwith an ordinal symbolization rule by comparing neighboring values in the time series. Complex networks have also been successfully employed for time series analysis [22–27]. Correlation graphs =-=[28, 29]-=-, recurrence graphs [30–32], and visibility graphs [33–37] have been shown to provide relevant information, for example, of early warning indicators of qualitative changes and abrupt transitions. Here... |

4 | Sanjuán MAF (2007) True and false forbidden patterns in deterministic and random dynamics. Europhys - JS, Zambrano |

3 |
F J andRobledoA 2012Analytical properties of horizontal visibility graphs in the Feigenbaum scenario Chaos 22 013109
- Luque, Lacasa, et al.
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Citation Context ..., in the limit of → ∞D , sp tends to the topological entropy [16]. In the visibility graph, a direct relationship between the network entropy and the LE can be established by using the Pesin identity =-=[36]-=-. Therefore, these results suggest that the network entropy can indeed be expected to capture nontrivial properties of the dynamics; however, determining a direct correspondence between different netw... |

2 | P andYoungK 1989 Inferring statistical complexity Phys - Crutchfield |

2 | T andAlbrecht K-F 1995 Entropy, transinformation andword distribution of information-carrying sequences Int - EbelingW |

2 | FinneyCEA 2003A review of symbolic analysis of experimental dataRev - DawaC |

2 | andHutt A 2013Detecting recurrence domains of dynamical systems by symbolic dynamics Phys - PB |

2 | Cabeza C,Marti AC andMasoller C 2013Characterizing the dynamics of coupled pendulums via symbolic time series analysis - Polsi |

2 | Saco PMandRossoOA2010Missing ordinal patterns in correlated noisesPhysicaA - LC |

2 | PlastinoA and FuentesMA2007Distinguishing noise from chaosPhys - RossoOA, MartinMT |

2 | S Y andVoss L J 2008Using permutation entropy tomeasure the electroencephalographic effects of sevoflurane Anesthesiology 109 - Li, Cui |

2 |
Ghasemi F, Stefanovska A,McClintock PVE andKantzH 2008Direction of coupling fromphases of interacting oscillators: a permutation information approachPhys
- Bahraminasab
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Citation Context ... highdimensional signals. Symbolic analysis has also proven to be useful for classifying different types of signals [9– 12] and, in bivariate analysis, for inferring the direction of information flow =-=[13, 14]-=-. The symbolic approach involves the transformation of a time series, x(t), into a sequence of symbols, s(t), by using an appropriated codification rule. A significant advantage of symbolization is it... |

2 |
PompeB 2002 Permutation entropy: a natural complexitymeasure for time series Phys
- Bandt
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Citation Context ...ime series x(t) into a sequence of symbols s(t) by using theOP representationwith symbols of lengthD. In this case, symbols are defined by considering groups ofD consecutive values in the time series =-=[15]-=-. There existD! differentOPs of lengthD. For example, forD=2 there are twoOPs: < +x t x t( ) ( 1) gives symbol ‘01’ and > +x t x t( ) ( 1) gives symbol ‘10’; forD= 3 there are six possibleOPs: < + < +... |

2 |
G and Pompe B 2002 Entropy of intervalmaps via permutationsNonlinearity 15
- Bandt, Keller
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Citation Context ...eviously been shown that for chaotic parameters and lowD values, sp behaves as the LE [15]. In addition, for piecewisemonotone intervalmaps, in the limit of → ∞D , sp tends to the topological entropy =-=[16]-=-. In the visibility graph, a direct relationship between the network entropy and the LE can be established by using the Pesin identity [36]. Therefore, these results suggest that the network entropy c... |

2 | LaufferH 2003 Symbolic analysis of high-dimensional time series 2003 - Keller |

2 | ProtopopescuVA andHively LM2004Detecting dynamical changes in time series using the permutation entropyPhys - YH, TungWW |

2 | 2007 Parameter selection for permutation entropymeasurements Int - StaniekMandLehnertz |

2 | RossoOA and PapoD 2012 Permutation entropy and itsmain biomedical and econophysics applications: a review Entropy 14 - ZaninM |

2 | SmallM2008 Superfamily phenomena andmotifs of networks induced from time series - XuX |

2 | ZhangK,Nakamura T and SmallM2008Characterizing pseudoperiodic time series through the complex network approachPhysicaD - Zhang, Sun, et al. |

2 |
ZhaoY andXueX 2014Characterizing systemdynamics with aweighted and directed network constructed from time series dataChaos 24 024402
- SunX
(Show Context)
Citation Context ...Deutsche PhysikalischeGesellschaft Our approach for defining the links as the TP between symbols was originally proposed byNicolis et al [22] and the use of ordinal analysis was proposed by Sun et al =-=[27]-=-; however, in [27] theweights of the linkswere not defined in terms of TPs (as in [22]), but rather, theywere defined as the number of times the pair of consecutive symbols (i, j) occurred in the time... |

2 |
den ToomM, FengQ,Kurths J andHernandez-Garcia E 2013 Interaction network based early warning indicators for the AtlanticMOC collapseGeophys
- MheenM, Gozolchiani
(Show Context)
Citation Context ...mputedwith an ordinal symbolization rule by comparing neighboring values in the time series. Complex networks have also been successfully employed for time series analysis [22–27]. Correlation graphs =-=[28, 29]-=-, recurrence graphs [30–32], and visibility graphs [33–37] have been shown to provide relevant information, for example, of early warning indicators of qualitative changes and abrupt transitions. Here... |

2 | ZouY,Donges J F,MarwanNandKurths J 2010Recurrence networks—a novel paradigm for nonlinear time series analysisNew - RV |

2 | RV, Rehfeld K,MarwanN, TrauthMHandKurths J 2011 Identification of dynamical transitions inmarine palaeoclimate records by recurrence network analysisNonlinear Proc. Geophys - Donges, Donner |

2 | S andKurths J 2013Recurrence plots 25 years later—Gaining confidence in dynamical transitions Europhys - MarwanN |

2 | F J andRobledoA 2011 Feigenbaumgraphs: a complex network perspective of chaos PLOSONE - Luque, Lacasa, et al. |

2 | Gómez J P andRobledoA 2013Horizontal visibility graphs generated by type-I intermittency Phys - AM, Luque, et al. |

2 |
andRossoOA2006Generalized statistical complexitymeasures: geometrical and analytical properties Physica A 369 439–62
- MartinMT
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Citation Context ...ults are consistent with a previous analysis of the complexity of the logisticmap, where the peak values of the various complexitymeasures analyzed occurred at intermediate values of themap parameter =-=[39]-=-. For the stochastic circlemap, sl and ac [figures 3(e) and (f)] reveal that the network is homogeneous (large link entropy accompanied by small asymmetry coefficient) for ≃k 0, at the locking transit... |

2 |
Prati F 2013VCSELs (Springer Series inOptical Sciences) ed RMichalzik pp 181–231
- Panajotov
(Show Context)
Citation Context ...ler range of values as comparedwith sn. 7 New J. Phys. 17 (2015) 023068 CMasoller et al polarization switching can be in part due to thermal effects (Joule heating) through a shift of the gainmaximum =-=[40]-=-. Also, small cavity anisotropies can play a role, as theVCSEL circular transverse geometry provides no polarization selectionmechanism. In addition,material birefringence, saturable dispersion, and a... |

2 |
SanMiguelM andAbrahamNB1997 Polarization properties of vertical-cavity surface-emitting lasers
- Martin-Regalado, Prati
- 2015
(Show Context)
Citation Context ...L circular transverse geometry provides no polarization selectionmechanism. In addition,material birefringence, saturable dispersion, and amicroscopic spin-flip relaxationmechanism can explain the PS =-=[41]-=-. Because various sources of noise are ubiquitous in laser systems (spontaneous emission noise, thermal and electrical noise), it is not possible to investigate experimentally the relative impact of s... |