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Volume 53 Issue 2
Jun.  2023
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Article Navigation >  Advances in Mechanics  > 2023  >  53(2): 357-394
Jin Y F, Xu P F, Li Y G, Ma J Z, Xu Y. Stochastic resonance of multi-stable dynamical systems: A review. Advances in Mechanics, 2023, 53(2): 357-394 doi: 10.6052/1000-0992-22-047
Citation: Jin Y F, Xu P F, Li Y G, Ma J Z, Xu Y. Stochastic resonance of multi-stable dynamical systems: A review. Advances in Mechanics, 2023, 53(2): 357-394 doi: 10.6052/1000-0992-22-047
shu

Stochastic resonance of multi-stable dynamical systems: A review

doi: 10.6052/1000-0992-22-047
  • 1.

    Department of Mechanics, Beijing Institute of Technology, Beijing 100081, China

  • 2.

    Department of Mathematics, Shanxi Agricultural University, Jinzhong 030801, Shanxi, China

  • 3.

    School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710072, China

  • 4.

    School of Mathematical Sciences, Shanxi University, Taiyuan 030006, China

  • 5.

    MOE Key Laboratory for Complexity Science in Aerospace, Northwestern Polytechnical University, Xi’an 710072, China

More Information
  • Corresponding author: hsux3@nwpu.edu.cn
  • Received Date: 2022-11-28
  • Accepted Date: 2023-02-27
    • Available Online: 2023-03-11
  • Publish Date: 2023-06-25
    Abstract
  • The nonlinear stochastic dynamical system has been an important subject in areas of mechanics, mathematics, engineering and so on, and finds various applications in different fields like mechanical engineering, aerospace engineering, ocean engineering, and biology. The multi-stable dynamical systems are conceptual nonlinear systems, coupling with stochastic excitations, which can exhibit complex dynamical behaviors, such as stochastic resonance and stochastic bifurcation. The stochastic resonance theory has been utilized effectively in many areas related to stochastic dynamics such as mechanical fault diagnosis, weak signal detection and vibration energy harvesting. This paper overviews the fundamental theories, methods and engineering applications of stochastic resonance in multi-stable dynamical systems. We introduce recent advances in theories and measure index of stochastic resonance via several classic examples of nonlinear dynamical systems. Then, we summarize the results of multi-stable dynamical systems under the excitation of different types of noise. The tri-stable and periodic systems are illustrated to show the occurrence principle, evolution mechanism and investigated techniques. Finally, three engineering applications of multi-stable dynamical systems are surveyed. Some open problems are presented to close this paper.

     

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