| Summary: | This work aims to address the P-bifurcation of a stochastic nonlinear system with fractional damping driven by Gaussian white noise. Based on a stochastic averaging method, a fractional damping stochastic nonlinear equation has been studied. Furthermore, the expressions of drift and diffusion coefficients of the Fokker–Planck equation (FPKE) have been obtained. The probability density function (PDF), the steady solution of FPKE, has also been derived. Then, PDFs of two fractional damping Morse oscillators have been obtained. One can note that the analytical results coincide with the results of numerical simulation. Importantly, stochastic P-bifurcation of a fractional damping stochastic nonlinear Morse oscillator has been further addressed and analyzed.
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