Version 1
: Received: 15 October 2024 / Approved: 15 October 2024 / Online: 29 October 2024 (10:58:09 CET)
How to cite:
Lin, Z.; Pattanayak, A. K. A Chaos Synchronization Diagnostic: Difference Time Series Peak Complexity (DTSPC). Preprints2024, 2024102283. https://doi.org/10.20944/preprints202410.2283.v1
Lin, Z.; Pattanayak, A. K. A Chaos Synchronization Diagnostic: Difference Time Series Peak Complexity (DTSPC). Preprints 2024, 2024102283. https://doi.org/10.20944/preprints202410.2283.v1
Lin, Z.; Pattanayak, A. K. A Chaos Synchronization Diagnostic: Difference Time Series Peak Complexity (DTSPC). Preprints2024, 2024102283. https://doi.org/10.20944/preprints202410.2283.v1
APA Style
Lin, Z., & Pattanayak, A. K. (2024). A Chaos Synchronization Diagnostic: Difference Time Series Peak Complexity (DTSPC). Preprints. https://doi.org/10.20944/preprints202410.2283.v1
Chicago/Turabian Style
Lin, Z. and Arjendu K. Pattanayak. 2024 "A Chaos Synchronization Diagnostic: Difference Time Series Peak Complexity (DTSPC)" Preprints. https://doi.org/10.20944/preprints202410.2283.v1
Abstract
Chaotic systems can exhibit completely different behaviors given only slightly different initial conditions, yet it is possible to synchronize them through appropriate coupling. A wide variety of behaviors – complete chaos, complete synchronization, phase synchronization, etc – across a variety of systems have been identified but rely on systems’ phase space portraits, which suppress important distinctions between very different behaviors and require access to the differential equations or the full time-series. In this paper, we introduce the Difference Time Series Peaks Complexity (DTSPC) algorithm. This uses ordinal patterns created from sampled time-series, focusing on the the behavior of ringing patterns in the difference time series to quantitatively distinguish a variety of synchronization behaviors based on the entropic complexity of the populations of various patterns. We present results from the paradigmatic case of coupled Lorenz systems, both identical and non-identical and across a range of parameters and show that this technique captures the diversity of possible synchronization, including non-monotonicity as a function of parameter as well as complicated boundaries between different regimes. Thus this ordinal pattern entropy analysis algorithm reveals and quantifies the complexity of chaos synchronization dynamics, and in particular captures transitional behaviors between different regimes.
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
