Entropy-based generating Markov partitions for complex systems.
@article{Rubido2018EntropybasedGM, title={Entropy-based generating Markov partitions for complex systems.}, author={Nicol{\'a}s Rubido and Celso Grebogi and Murilo S. Baptista}, journal={Chaos}, year={2018}, volume={28 3}, pages={ 033611 } }
Finding the correct encoding for a generic dynamical system's trajectory is a complicated task: the symbolic sequence needs to preserve the invariant properties from the system's trajectory. In theory, the solution to this problem is found when a Generating Markov Partition (GMP) is obtained, which is only defined once the unstable and stable manifolds are known with infinite precision and for all times. However, these manifolds usually form highly convoluted Euclidean sets, are a priori…
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References
SHOWING 1-10 OF 27 REFERENCES
Estimating generating partitions of chaotic systems by unstable periodic orbits
- Computer SciencePhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 2000
A general, dimension-independent, and efficient approach based on optimizing a set of proximity functions defined with respect to periodic orbits to obtain the approximate location of the generating partition for the Ikeda-Hammel-Jones-Moloney map.
Topological and metric properties of Hénon-type strange attractors.
- MathematicsPhysical review. A, General physics
- 1988
The set of all periodic points of H\'enon-type mappings is used to develop a theory of the topological and metric properties of their attractors, and the singularity spectrum f(\ensuremath{\alpha}) is computed.
Ergodic theory of chaos and strange attractors
- Physics
- 1985
Physical and numerical experiments show that deterministic noise, or chaos, is ubiquitous. While a good understanding of the onset of chaos has been achieved, using as a mathematical tool the…
How does a choice of Markov partition affect the resultant symbolic dynamics?
- MathematicsChaos
- 2010
It is shown that if a Markov partition is regarded as a map-refinement of the other Markov partitions, that is, a concept the authors newly introduce in this article, one can uniquely translate a set of symbolic sequences by oneMarkov partition to those by the other or vice versa.
Clustering, coding, switching, hierarchical ordering, and control in a network of chaotic elements
- Physics
- 1990
Transcripts: an algebraic approach to coupled time series.
- Computer ScienceChaos
- 2012
This paper revisits the concept of transcript between two symbolic representations, generalize it to N representations, and derive some general properties of ordinal symbolic dynamics, and uses transcripts to define two complexity indicators of coupled dynamics.
Estimating good discrete partitions from observed data: symbolic false nearest neighbors.
- Computer SciencePhysical review letters
- 2003
This paper introduces a statistic and algorithm to refine empirical partitions for symbolic state reconstruction, and optimizes an essential property of a generating partition, avoiding topological degeneracies, by minimizing the number of "symbolic false nearest neighbors".
Validity of threshold-crossing analysis of symbolic dynamics from chaotic time series
- PhysicsPhysical review letters
- 2000
A practical and popular technique to extract the symbolic dynamics from experimentally measured chaotic time series is the threshold-crossing method, by which an arbitrary partition is utilized for…
Generating partition for the standard map.
- MathematicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1995
A procedure to obtain the symbolic dynamics for conservative dynamical systems is introduced with reference to the standard map in a strongly chaotic regime based on the construction of a generating partition from homoclinic tangencies and fibers of invariant manifolds.
Trapping phenomenon attenuates tipping points for limit cycles
- Physics
- 2016
Nonlinear dynamical systems may be exposed to tipping points, critical thresholds at which small changes in the external inputs or in the systems parameters abruptly shift the system to an…