Stochastic response and bifurcation of periodically driven nonlinear oscillators by the generalized cell mapping method

Qun Han, Wei Xu and Jian-Qiao Sun

Physica A: Statistical Mechanics and its Applications, 2016, vol. 458, issue C, 115-125

Abstract: The stochastic response of nonlinear oscillators under periodic and Gaussian white noise excitations is studied with the generalized cell mapping based on short-time Gaussian approximation (GCM/STGA) method. The solutions of the transition probability density functions over a small fraction of the period are constructed by the STGA scheme in order to construct the GCM over one complete period. Both the transient and steady-state probability density functions (PDFs) of a smooth and discontinuous (SD) oscillator are computed to illustrate the application of the method. The accuracy of the results is verified by direct Monte Carlo simulations. The transient responses show the evolution of the PDFs from being Gaussian to non-Gaussian. The effect of a chaotic saddle on the stochastic response is also studied. The stochastic P-bifurcation in terms of the steady-state PDFs occurs with the decrease of the smoothness parameter, which corresponds to the deterministic pitchfork bifurcation.

Keywords: Stochastic bifurcation; SD oscillator; Periodic force; Generalized cell mapping method; Short-time Gaussian approximation (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:458:y:2016:i:c:p:115-125

DOI: 10.1016/j.physa.2016.04.006

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