Search for optimal parameters in a recurrence analysis of the Duffing system with varying damping
•The Duffing system is investigated by recurrence plot-based numerical methods.•RQA measures are calculated for different values of the method parameters.•The threshold parameter is tuned by comparing RQA variables with Lyapunov exponents.•Appropriate selection of parameters gives invariant RQA resu...
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| Published in: | Communications in nonlinear science & numerical simulation Vol. 84; p. 105192 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
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| Abstract | •The Duffing system is investigated by recurrence plot-based numerical methods.•RQA measures are calculated for different values of the method parameters.•The threshold parameter is tuned by comparing RQA variables with Lyapunov exponents.•Appropriate selection of parameters gives invariant RQA results.
Starting from the 1990s, recurrence analysis is more and more widely used in the study of dynamic systems. Although this method provides a great deal of information, its results clearly depend on key parameters, which significantly limits and hinders its application. In this work, we examine this problem by analyzing the Duffing system in which the volatility of dynamics is caused by a linear change in the damping factor value. The study shows how the classical recurrence measures depend on key parameters such as the density of vector time series and the threshold parameter. Comparing the recurrence analysis results with bifurcation diagrams and Lyapunov exponents, we are looking for a threshold parameter value for which the recurrence variables best reflect changes in the Duffing system dynamics. |
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| AbstractList | Starting from the 1990s, recurrence analysis is more and more widely used in the study of dynamic systems. Although this method provides a great deal of information, its results clearly depend on key parameters, which significantly limits and hinders its application. In this work, we examine this problem by analyzing the Duffing system in which the volatility of dynamics is caused by a linear change in the damping factor value. The study shows how the classical recurrence measures depend on key parameters such as the density of vector time series and the threshold parameter. Comparing the recurrence analysis results with bifurcation diagrams and Lyapunov exponents, we are looking for a threshold parameter value for which the recurrence variables best reflect changes in the Duffing system dynamics. •The Duffing system is investigated by recurrence plot-based numerical methods.•RQA measures are calculated for different values of the method parameters.•The threshold parameter is tuned by comparing RQA variables with Lyapunov exponents.•Appropriate selection of parameters gives invariant RQA results. Starting from the 1990s, recurrence analysis is more and more widely used in the study of dynamic systems. Although this method provides a great deal of information, its results clearly depend on key parameters, which significantly limits and hinders its application. In this work, we examine this problem by analyzing the Duffing system in which the volatility of dynamics is caused by a linear change in the damping factor value. The study shows how the classical recurrence measures depend on key parameters such as the density of vector time series and the threshold parameter. Comparing the recurrence analysis results with bifurcation diagrams and Lyapunov exponents, we are looking for a threshold parameter value for which the recurrence variables best reflect changes in the Duffing system dynamics. |
| ArticleNumber | 105192 |
| Author | Gregorczyk, M. Rysak, A. Tra̧bka-Wiȩcław, K. Zaprawa, P. |
| Author_xml | – sequence: 1 givenname: A. orcidid: 0000-0001-9631-9785 surname: Rysak fullname: Rysak, A. email: a.rysak@pollub.pl – sequence: 2 givenname: M. surname: Gregorczyk fullname: Gregorczyk, M. email: m.gregorczyk@pollub.pl – sequence: 3 givenname: P. surname: Zaprawa fullname: Zaprawa, P. email: p.zaprawa@pollub.pl – sequence: 4 givenname: K. surname: Tra̧bka-Wiȩcław fullname: Tra̧bka-Wiȩcław, K. email: k.trabka@pollub.pl |
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| Cites_doi | 10.1152/jappl.1994.76.2.965 10.1103/PhysRevE.65.021102 10.1016/j.physrep.2006.11.001 10.1140/epjst/e2008-00833-5 10.1142/S0218127411029008 10.1016/j.chaos.2006.07.059 10.1016/S0167-2789(96)00216-3 10.1103/RevModPhys.57.617 10.1016/S0167-2789(97)82003-9 10.1103/PhysRevE.81.015101 10.1098/rspa.2003.1183 10.1209/0295-5075/4/9/004 10.1016/S0167-2789(02)00586-9 10.1016/j.chaos.2007.09.093 10.1016/0375-9601(92)90426-M 10.1063/1.5024914 10.1016/S0375-9601(02)00436-X 10.1016/j.ymssp.2016.08.037 |
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| Snippet | •The Duffing system is investigated by recurrence plot-based numerical methods.•RQA measures are calculated for different values of the method parameters.•The... Starting from the 1990s, recurrence analysis is more and more widely used in the study of dynamic systems. Although this method provides a great deal of... |
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| SubjectTerms | Bifurcation Bifurcations Damping Duffing system Dynamical systems Liapunov exponents Nonlinear dynamics Parameter estimation Parameters Recurrence plots System dynamics Time series Volatility |
| Title | Search for optimal parameters in a recurrence analysis of the Duffing system with varying damping |
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