Stability and bifurcation in a stochastic vocal folds model

•Stability and bifurcation in a stochastic vocal folds model are investigated. The underlying deterministic model used is the nonlinear two-dimensional model proposed by Lucero [3].•This is proved that under some conditions the unique equilibrium point of the stochastic vocal folds model is stable.•By varying some parameters such as noise intensity, the model undergoes P-bifurcation.•We present some theorems that give necessary and sufficient conditions for stability at equilibrium point and stochastic bifurcation.•We use Euler-Maruyama method as a simple numerical method to stochastic systems and present some numerical simulation to illustrate the established results. In this paper, the stability and bifurcation in a class of stochastic vocal folds dynamical model are investigated. We use polar coordinate, Taylor expansion and stochastic averaging method to transform our classic system into an Itô averaging diffusion system. Also, we recall some theorems that give us some conditions which leads to sufficient conditions on drift and diffusion coefficients for stochastic stability and P-bifurcation of the model. Finally, numerical simulations are presented to show the effects of the noise intensity and illustrate our theoretical results.