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Analysis of stochastic resonance in coupled oscillator with fractional damping disturbed by polynomial dichotomous noise

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Abstract

Investigation on particle synchronization behavior and different kinds of stochastic resonance mechanism is reported in a fractional-order stochastic coupled system, which endures an external periodic excitation and polynomial asymmetric dichotomous noise damping disturbance. An extending of the method of stochastic averaging, the fractional Shapiro–Loginov formula and fractional Laplace transformation law are utilized, to determine the synchronization behavior between two coupled oscillators. The first moment of steady-state response and the output signal amplitude of the system are obtained in an analytical way, along with the stability condition. The crucial role of damping order and intrinsic frequency in stochastic resonance induced by noise intensity is explored, confirming the necessity of studying damping order falling in (1, 2). Due to the presence of nonlinear dichotomous colored noise, fresh phenomena of stochastic resonance and hypersensitive response induced by variation of external excitation frequency are found, where much more novel dynamical behaviors emerge than the non-disturbance case. It is confirmed that bimodal stochastic resonance only occurs for slow switching noise, with the damping order close to the parameter region of 0 or 2. For parameter-induced generalized stochastic resonance, explicit expressions of the critical damping strength corresponding to the optimal peak point of output amplitude are derived for the first time. By which different stochastic resonance patterns of the system under slow and fast switching noise perturbation are predicted successfully. In addition, the parametric effect and action mechanism of damping order on stochastic resonance are discussed in detail.

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Funding

This work was supported by National Natural Science Foundation of China (No.12002194; No.12072178); Project No.ZR2020MA054 supported by Shandong Provincial Natural Science Foundation.

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Authors and Affiliations

  1. Division of Dynamics and Control, School of Mathematics and Statistics, Shandong University of Technology, Zibo, 255000, China

    Zhi Yan & Huatao Chen

  2. Department of Applied Mathematics and Statistics, Technical University of Cartagena, Hospital de Marina, 30203, Cartagena, Spain

    Juan L. G. Guirao

  3. Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

    Juan L. G. Guirao & T. Saeed

  4. State Key Laboratory of Mechanics and Control of Mechanical Structures, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Xianbin Liu

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  1. Zhi Yan
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Correspondence to Huatao Chen.

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Yan, Z., Guirao, J.L.G., Saeed, T. et al. Analysis of stochastic resonance in coupled oscillator with fractional damping disturbed by polynomial dichotomous noise. Nonlinear Dyn 110, 1233–1251 (2022). https://doi.org/10.1007/s11071-022-07688-w

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