Quasiperiodic graphs at the onset of chaos
arXiv:1312.3089 · doi:10.1103/PhysRevE.88.062918
Abstract
We examine the connectivity fluctuations across networks obtained when the horizontal visibility (HV) algorithm is used on trajectories generated by nonlinear circle maps at the quasiperiodic transition to chaos. The resultant HV graph is highly anomalous as the degrees fluctuate at all scales with amplitude that increases with the size of the network. We determine families of Pesin-like identities between entropy growth rates and generalized graph-theoretical Lyapunov exponents. An irrational winding number with pure periodic continued fraction characterizes each family. We illustrate our results for the so-called golden, silver and bronze numbers.
arXiv commentarXiv admin note: text overlap with arXiv:1205.1902
References in corpus (15)
- From time series to complex networks: the visibility graph
- Recurrence networks - A novel paradigm for nonlinear time series analysis
- Recurrence-based time series analysis by means of complex network methods
- Kolmogorov-Sinai entropy-rate vs. physical entropy
- The Geometry of Chaotic Dynamics -- A Complex Network Perspective
- Nonextensive Pesin identity. Exact renormalization group analytical results for the dynamics at the edge of chaos of the logistic map
- Feigenbaum graphs: a complex network perspective of chaos
- Tsallis' q index and Mori's q phase transitions at edge of chaos
- Analytical properties of horizontal visibility graphs in the Feigenbaum scenario
- Horizontal Visibility graphs generated by type-I intermittency
- Incidence of nonextensive thermodynamics in temporal scaling at Feigenbaum points
- Quasiperiodic graphs: structural design, scaling and entropic properties
- Feigenbaum graphs at the onset of chaos
- Fluctuating dynamics at the quasiperiodic onset of chaos, Tsallis q-statistics and Mori's q-phase thermodynamics
- Leonhard Euler and a q-analogue of the logarithm