Dynamic Behaviors Analysis of Asymmetric Stochastic Delay Differential Equations with Noise and Application to Weak Signal Detection
This paper presents the dynamic behaviors of a second-order asymmetric stochastic delay system with a Duffing oscillator as well as through the detection of weak signals, which are analyzed theoretically and numerically. The dynamic behaviors of the asymmetric system are analyzed based on the stocha...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-11-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/11/11/1428 |
| _version_ | 1811297776596680704 |
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| author | Qiubao Wang Xing Zhang Yuejuan Yang |
| author_facet | Qiubao Wang Xing Zhang Yuejuan Yang |
| author_sort | Qiubao Wang |
| collection | DOAJ |
| description | This paper presents the dynamic behaviors of a second-order asymmetric stochastic delay system with a Duffing oscillator as well as through the detection of weak signals, which are analyzed theoretically and numerically. The dynamic behaviors of the asymmetric system are analyzed based on the stochastic center manifold, together with Hopf bifurcation. Numerical analysis revealed that the time delay could enhance the noise immunity of the asymmetric system so as to enhance the asymmetric system’s ability to detect weak signals. The frequency of the weak signal under noise excitation was detected through the ‘act-and-wait’ method. The small amplitude was detected through the transition from the chaotic to the periodic state. Theoretical analysis and numerical simulation indicate that the application of the asymmetric Duffing oscillator with delay to detect weak signal is feasible. |
| first_indexed | 2024-04-13T06:09:16Z |
| format | Article |
| id | doaj.art-cd61f295bcfd4b14bdf6d7669dbe54db |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-13T06:09:16Z |
| publishDate | 2019-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-cd61f295bcfd4b14bdf6d7669dbe54db2022-12-22T02:59:07ZengMDPI AGSymmetry2073-89942019-11-011111142810.3390/sym11111428sym11111428Dynamic Behaviors Analysis of Asymmetric Stochastic Delay Differential Equations with Noise and Application to Weak Signal DetectionQiubao Wang0Xing Zhang1Yuejuan Yang2Department of Mathematical and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043, ChinaDepartment of Mathematical and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043, ChinaDepartment of Mathematical and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043, ChinaThis paper presents the dynamic behaviors of a second-order asymmetric stochastic delay system with a Duffing oscillator as well as through the detection of weak signals, which are analyzed theoretically and numerically. The dynamic behaviors of the asymmetric system are analyzed based on the stochastic center manifold, together with Hopf bifurcation. Numerical analysis revealed that the time delay could enhance the noise immunity of the asymmetric system so as to enhance the asymmetric system’s ability to detect weak signals. The frequency of the weak signal under noise excitation was detected through the ‘act-and-wait’ method. The small amplitude was detected through the transition from the chaotic to the periodic state. Theoretical analysis and numerical simulation indicate that the application of the asymmetric Duffing oscillator with delay to detect weak signal is feasible.https://www.mdpi.com/2073-8994/11/11/1428stochasticdelayasymmetric systemweak signals |
| spellingShingle | Qiubao Wang Xing Zhang Yuejuan Yang Dynamic Behaviors Analysis of Asymmetric Stochastic Delay Differential Equations with Noise and Application to Weak Signal Detection Symmetry stochastic delay asymmetric system weak signals |
| title | Dynamic Behaviors Analysis of Asymmetric Stochastic Delay Differential Equations with Noise and Application to Weak Signal Detection |
| title_full | Dynamic Behaviors Analysis of Asymmetric Stochastic Delay Differential Equations with Noise and Application to Weak Signal Detection |
| title_fullStr | Dynamic Behaviors Analysis of Asymmetric Stochastic Delay Differential Equations with Noise and Application to Weak Signal Detection |
| title_full_unstemmed | Dynamic Behaviors Analysis of Asymmetric Stochastic Delay Differential Equations with Noise and Application to Weak Signal Detection |
| title_short | Dynamic Behaviors Analysis of Asymmetric Stochastic Delay Differential Equations with Noise and Application to Weak Signal Detection |
| title_sort | dynamic behaviors analysis of asymmetric stochastic delay differential equations with noise and application to weak signal detection |
| topic | stochastic delay asymmetric system weak signals |
| url | https://www.mdpi.com/2073-8994/11/11/1428 |
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