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Article

A Novel Measure Inspired by Lyapunov Exponents for the Characterization of Dynamics in State-Transition Networks

1
Department of Physics, Babes-Bolyai University, 400084 Cluj-Napoca, Romania
2
Network Science Lab, Transylvanian Institute of Neuroscience, 400157 Cluj-Napoca, Romania
*
Authors to whom correspondence should be addressed.
Entropy 2021, 23(1), 103; https://doi.org/10.3390/e23010103
Received: 15 December 2020 / Revised: 6 January 2021 / Accepted: 7 January 2021 / Published: 12 January 2021
The combination of network sciences, nonlinear dynamics and time series analysis provides novel insights and analogies between the different approaches to complex systems. By combining the considerations behind the Lyapunov exponent of dynamical systems and the average entropy of transition probabilities for Markov chains, we introduce a network measure for characterizing the dynamics on state-transition networks with special focus on differentiating between chaotic and cyclic modes. One important property of this Lyapunov measure consists of its non-monotonous dependence on the cylicity of the dynamics. Motivated by providing proper use cases for studying the new measure, we also lay out a method for mapping time series to state transition networks by phase space coarse graining. Using both discrete time and continuous time dynamical systems the Lyapunov measure extracted from the corresponding state-transition networks exhibits similar behavior to that of the Lyapunov exponent. In addition, it demonstrates a strong sensitivity to boundary crisis suggesting applicability in predicting the collapse of chaos. View Full-Text
Keywords: Lyapunov exponents; state-transition networks; time series analysis; dynamical systems Lyapunov exponents; state-transition networks; time series analysis; dynamical systems
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Figure 1

  • Externally hosted supplementary file 1
    Link: https://github.com/schbence/stn-lyapunov
    Description: The Python code developed to construct the state-transition networks and compute Lyapunov measure are available online at https://github.com/schbence/stn-lyapunov
MDPI and ACS Style

Sándor, B.; Schneider, B.; Lázár, Z.I.; Ercsey-Ravasz, M. A Novel Measure Inspired by Lyapunov Exponents for the Characterization of Dynamics in State-Transition Networks. Entropy 2021, 23, 103. https://doi.org/10.3390/e23010103

AMA Style

Sándor B, Schneider B, Lázár ZI, Ercsey-Ravasz M. A Novel Measure Inspired by Lyapunov Exponents for the Characterization of Dynamics in State-Transition Networks. Entropy. 2021; 23(1):103. https://doi.org/10.3390/e23010103

Chicago/Turabian Style

Sándor, Bulcsú, Bence Schneider, Zsolt I. Lázár, and Mária Ercsey-Ravasz. 2021. "A Novel Measure Inspired by Lyapunov Exponents for the Characterization of Dynamics in State-Transition Networks" Entropy 23, no. 1: 103. https://doi.org/10.3390/e23010103

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