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Dynamic Behaviors Analysis of Asymmetric Stochastic Delay Differential Equations with Noise and Application to Weak Signal Detection

Department of Mathematical and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China
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Symmetry 2019, 11(11), 1428; https://doi.org/10.3390/sym11111428
Received: 24 October 2019 / Revised: 11 November 2019 / Accepted: 15 November 2019 / Published: 19 November 2019
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. View Full-Text
Keywords: stochastic; delay; asymmetric system; weak signals stochastic; delay; asymmetric system; weak signals
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Wang, Q.; Zhang, X.; Yang, Y. Dynamic Behaviors Analysis of Asymmetric Stochastic Delay Differential Equations with Noise and Application to Weak Signal Detection. Symmetry 2019, 11, 1428.

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