Dynamical Analysis for a General Jerky Equation with Random Excitation (Journal of Nonlinear Modeling and Analysis, 2024)
A general jerky equation with random excitation is investigated inthis paper. Before introducing the random excitation term, the equation is reduced to a two-dimensional model when undergoing a Hopf bifurcation. Thenthe model with the parametric excitation and external excitation is convertedto a stochastic differential equation with singularity based on the stochastic average theory. For the equation, its dynamical behaviors are analyzedin different parameters' spaces, including the stability, stochastic bifurcationand stationary solution. Besides, numerical simulations are given to show theasymptotic behavior of the stationary solution.