A Novel Measure Inspired by Lyapunov Exponents for the Characterization of Dynamics in State-Transition Networks
Abstract
:1. Introduction
2. Results
2.1. State-Transition Networks
2.2. Lyapunov Measure
2.2.1. Properties of the Lyapunov Measure
2.2.2. Analytical Study of the Lyapunov Measure
2.3. Time Series Analysis with STNs
Construction of STNs
2.4. Network Measures
3. Materials and Methods
3.1. Discrete- and Continuous-Time Dynamical Systems
3.2. Phase-Space Discretization and Poincare Sections
3.3. Ensemble Averages and Asymptotic Behavior
4. Discussion
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A. Offset at c = 0 in the Lyapunov Measure According to the Random Network Model
Appendix B. Location and Size of the Maximum in the Lyapunov Measure According to the Random Network Model
Appendix C. Distribution of Uniform Random Numbers Normalized over Large Sets
Appendix D. Insight into the Emergence of Precursor Peaks
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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
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 StyleSándor, 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