A General Metric for the Similarity of Both Stochastic and Deterministic System Dynamics
Many problems in the study of dynamical systems—including identification of effective order, detection of nonlinearity or chaos, and change detection—can be reframed in terms of assessing the similarity between dynamical systems or between a given dynamical system and a reference. We introduce a gen...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-09-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/23/9/1191 |
| _version_ | 1797519435582406656 |
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| author | Colin Shea-Blymyer Subhradeep Roy Benjamin Jantzen |
| author_facet | Colin Shea-Blymyer Subhradeep Roy Benjamin Jantzen |
| author_sort | Colin Shea-Blymyer |
| collection | DOAJ |
| description | Many problems in the study of dynamical systems—including identification of effective order, detection of nonlinearity or chaos, and change detection—can be reframed in terms of assessing the similarity between dynamical systems or between a given dynamical system and a reference. We introduce a general metric of dynamical similarity that is well posed for both stochastic and deterministic systems and is informative of the aforementioned dynamical features even when only partial information about the system is available. We describe methods for estimating this metric in a range of scenarios that differ in respect to contol over the systems under study, the deterministic or stochastic nature of the underlying dynamics, and whether or not a fully informative set of variables is available. Through numerical simulation, we demonstrate the sensitivity of the proposed metric to a range of dynamical properties, its utility in mapping the dynamical properties of parameter space for a given model, and its power for detecting structural changes through time series data. |
| first_indexed | 2024-03-10T07:41:46Z |
| format | Article |
| id | doaj.art-9acf078e30e44c608b61eee673ad1c68 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T07:41:46Z |
| publishDate | 2021-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-9acf078e30e44c608b61eee673ad1c682023-11-22T12:58:03ZengMDPI AGEntropy1099-43002021-09-01239119110.3390/e23091191A General Metric for the Similarity of Both Stochastic and Deterministic System DynamicsColin Shea-Blymyer0Subhradeep Roy1Benjamin Jantzen2School of Electrical Engineering and Computer Science, Oregon State University, Corvallis, OR 97331, USADepartment of Mechanical Engineering, Embry-Riddle Aeronautical University, Daytona Beach, FL 32114, USADepartment of Philosophy, Virginia Tech, Blacksbug, VA 24060, USAMany problems in the study of dynamical systems—including identification of effective order, detection of nonlinearity or chaos, and change detection—can be reframed in terms of assessing the similarity between dynamical systems or between a given dynamical system and a reference. We introduce a general metric of dynamical similarity that is well posed for both stochastic and deterministic systems and is informative of the aforementioned dynamical features even when only partial information about the system is available. We describe methods for estimating this metric in a range of scenarios that differ in respect to contol over the systems under study, the deterministic or stochastic nature of the underlying dynamics, and whether or not a fully informative set of variables is available. Through numerical simulation, we demonstrate the sensitivity of the proposed metric to a range of dynamical properties, its utility in mapping the dynamical properties of parameter space for a given model, and its power for detecting structural changes through time series data.https://www.mdpi.com/1099-4300/23/9/1191nonlinearitymodel selectionchaos detectionchange detectionmodel behavior mappingdynamical similarity |
| spellingShingle | Colin Shea-Blymyer Subhradeep Roy Benjamin Jantzen A General Metric for the Similarity of Both Stochastic and Deterministic System Dynamics Entropy nonlinearity model selection chaos detection change detection model behavior mapping dynamical similarity |
| title | A General Metric for the Similarity of Both Stochastic and Deterministic System Dynamics |
| title_full | A General Metric for the Similarity of Both Stochastic and Deterministic System Dynamics |
| title_fullStr | A General Metric for the Similarity of Both Stochastic and Deterministic System Dynamics |
| title_full_unstemmed | A General Metric for the Similarity of Both Stochastic and Deterministic System Dynamics |
| title_short | A General Metric for the Similarity of Both Stochastic and Deterministic System Dynamics |
| title_sort | general metric for the similarity of both stochastic and deterministic system dynamics |
| topic | nonlinearity model selection chaos detection change detection model behavior mapping dynamical similarity |
| url | https://www.mdpi.com/1099-4300/23/9/1191 |
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