A Chaos Synchronization Diagnostic: Difference Time Series Peak Complexity (DTSPC)
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 syst...
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MDPI AG
2024-12-01
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| Online Access: | https://www.mdpi.com/1099-4300/26/12/1085 |
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| author | Zhe Lin Arjendu K. Pattanayak |
| author_facet | Zhe Lin Arjendu K. Pattanayak |
| author_sort | Zhe Lin |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-f139fac1b04b411583e22899f2a5d4c2 |
| institution | Kabale University |
| issn | 1099-4300 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj-art-f139fac1b04b411583e22899f2a5d4c22024-12-27T14:25:09ZengMDPI AGEntropy1099-43002024-12-012612108510.3390/e26121085A Chaos Synchronization Diagnostic: Difference Time Series Peak Complexity (DTSPC)Zhe Lin0Arjendu K. Pattanayak1United World College Changshu China, Suzhou 215500, ChinaDepartment of Physics and Astronomy, Carleton College, Northfield, MN 55057, USAChaotic 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.https://www.mdpi.com/1099-4300/26/12/1085chaossynchronizationentropy |
| spellingShingle | Zhe Lin Arjendu K. Pattanayak A Chaos Synchronization Diagnostic: Difference Time Series Peak Complexity (DTSPC) Entropy chaos synchronization entropy |
| title | A Chaos Synchronization Diagnostic: Difference Time Series Peak Complexity (DTSPC) |
| title_full | A Chaos Synchronization Diagnostic: Difference Time Series Peak Complexity (DTSPC) |
| title_fullStr | A Chaos Synchronization Diagnostic: Difference Time Series Peak Complexity (DTSPC) |
| title_full_unstemmed | A Chaos Synchronization Diagnostic: Difference Time Series Peak Complexity (DTSPC) |
| title_short | A Chaos Synchronization Diagnostic: Difference Time Series Peak Complexity (DTSPC) |
| title_sort | chaos synchronization diagnostic difference time series peak complexity dtspc |
| topic | chaos synchronization entropy |
| url | https://www.mdpi.com/1099-4300/26/12/1085 |
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