多稳态动力系统中随机共振的研究进展

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 tristable 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.