期刊
出版社
ROYAL SOC
DOI: 10.1098/rsta.2020.0229
关键词
stochastic systems; Ito calculus; Fokker-Plank equation; deterministic approach; high-frequency excitations
资金
- Russian Science Foundation [17-79-30056]
- Russian Science Foundation [17-79-30056] Funding Source: Russian Science Foundation
This paper discusses the feasibility of applying a deterministic approach to stochastic systems, including revisiting traditional nonlinear bistable systems, considering dynamic systems with multiplicative noise, and studying oscillatory systems with nonlinear damping. The results indicate that replacing stochastic excitations with deterministic ones is effective in analyzing these systems.
Adding noise to a system can 'improve' its dynamic behaviour, for example, it can increase its response or signal-to-noise ratio. The corresponding phenomenon, called stochastic resonance, has found numerous applications in physics, neuroscience, biology, medicine and mechanics. Replacing stochastic excitations with high-frequency ones was shown to be a viable approach to analysing several linear and nonlinear dynamic systems. For these systems, the influence of the stochastic and high-frequency excitations appears to be qualitatively similar. The present paper concerns the discussion of the applicability of this 'deterministic' approach to stochastic systems. First, the conventional nonlinear bi-stable system is briefly revisited. Then dynamical systems with multiplicative noise are considered and the validity of replacing stochastic excitations with deterministic ones for such systems is discussed. Finally, we study oscillatory systems with nonlinear damping and analyse the effects of stochastic and deterministic excitations on such systems. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 1)'.
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