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Affiliation of Author(s):航空学院

Title of Paper:On the Stochastic Dynamical Behaviors of a Nonlinear Oscillator Under Combined Real Noise and Harmonic Excitations

Journal:JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS

Key Words:DELAYED FEEDBACK-CONTROL 1ST-PASSAGE FAILURE LYAPUNOV EXPONENT COLORED NOISE BAND NOISE DRIVEN SYSTEMS STABILITY PERTURBATIONS

Abstract:The exit problem and global stability of a nonlinear oscillator excited by an ergodic real noise and harmonic excitations are examined. The real noise is assumed to be a scalar stochastic function of an n-dimensional Ornstein-Uhlenbeck vector process which is the output of a linear filter system. Due to the existence of t-dependent excitation, two two-dimensional Fokker-Planck-Kolmogorov (FPK) equations governing the van der Pol variables process and the amplitude-phase process, respectively, are obtained and discussed through a perturbation method and the spectrum representations of the FPK operator and its adjoint operator of the linear filter system, while the detailed balance condition and the strong mixing condition are removed. Based on these FPK equations, the global properties of one-dimensional nonlinear oscillators with external or (and) internal periodic excitations under external or (and) internal real noises can be examined. Finally, a Duffing oscillator excited by a parametric real noise and parametric harmonic excitations is presented as an example, and the mean first-passage time (MFPT) about the oscillator's exit behavior between limit cycles is obtained under both wide-band noise and narrow-band noise excitations. The analytical result is verified by digital simulation.

ISSN No.:1555-1423

Translation or Not:no

Date of Publication:2017-05-01

Co-author:Kong, Chen,陈朕

Correspondence Author:lxb