Ordinal Analysis of Complexity in 2D Chaotic Maps
Faculty Mentor
Andres Aragoneses
Document Type
Poster
Start Date
10-5-2023 11:15 AM
End Date
10-5-2023 1:00 PM
Location
PUB NCR
Department
Physics
Abstract
Effectively identifying and characterizing the various dynamics present in complex and chaotic systems is naturally a complicated task which becomes increasingly difficult to do with systems involving multiple spatial dimensions and parameters. Here, we extend ordinal methods of analysis to 2-D iterative systems, focusing on the Hénon map. We utilize the technique of ordinal patterns to characterize the dynamics of each time series and use heat maps to visualize and identify dynamical regimes and symmetries in a selected region of a and b forming a parameter space. Temporal And Reversible DYnamical Symmetry (TARDYS) quantifiers are constructed to evaluate two identified approximate symmetries between ordinal patterns, and we show that these symmetries are strongly correlated throughout the space. We also calculate Permutation Entropy (PE) and Fisher’s Information Measure (FIM) as measures of the long-term and short-term complexity, respectively, of the Hénon map, allowing us to better distinguish and identify separate dynamical regimes present in the parameter space.
Recommended Citation
Novak, Benjamin, "Ordinal Analysis of Complexity in 2D Chaotic Maps" (2023). 2023 Symposium. 12.
https://dc.ewu.edu/srcw_2023/res_2023/p2_2023/12
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Ordinal Analysis of Complexity in 2D Chaotic Maps
PUB NCR
Effectively identifying and characterizing the various dynamics present in complex and chaotic systems is naturally a complicated task which becomes increasingly difficult to do with systems involving multiple spatial dimensions and parameters. Here, we extend ordinal methods of analysis to 2-D iterative systems, focusing on the Hénon map. We utilize the technique of ordinal patterns to characterize the dynamics of each time series and use heat maps to visualize and identify dynamical regimes and symmetries in a selected region of a and b forming a parameter space. Temporal And Reversible DYnamical Symmetry (TARDYS) quantifiers are constructed to evaluate two identified approximate symmetries between ordinal patterns, and we show that these symmetries are strongly correlated throughout the space. We also calculate Permutation Entropy (PE) and Fisher’s Information Measure (FIM) as measures of the long-term and short-term complexity, respectively, of the Hénon map, allowing us to better distinguish and identify separate dynamical regimes present in the parameter space.
