Year: 2024
Type: article
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 trajectories, which suppress important distinctions between very different behaviors and require access to the differential equations. In this paper, we introduce the Difference Time Series Peak Complexity (DTSPC) algorithm, a technique using entropy as a tool to quantitatively measure synchronization. Specifically, this uses peak pattern complexity created from sampled time series, focusing on the behavior of ringing patterns in the difference time series to 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 peak pattern entropic analysis algorithm reveals and quantifies the complexity of chaos synchronization dynamics, and in particular captures transitional behaviors between different regimes.
Source: Entropy
DOI: 10.3390/e26121085
Authors: Zhe Lin, Arjendu K. Pattanayak
Institutions: United World College Changshu China, Carleton College
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,955
OpenAlex ID: W4405333535