Stochastic stability of variable-mass Duffing oscillator with mass disturbance modeled as Gaussian white noise

Asymptotic stability of a nonlinear energy harvester with mass disturbance undergoing Markovian jump

“…It has been proved that λ is an approximation of the largest Lyapunov exponent of the system (8) [32]. Thus, a necessary and sufficient condition for the asymptotic stability with probability one of the trivial solutions of system (8) is λ < 0.…”

“…The stochastic resonance for an oscillator with stochastic mass and stochastic damping was investigated and the stochastic mass was found that can generate a rich variety of non-equilibrium cooperation phenomena by Huang [30]. The stochastic stationary response and stochastic stability of a Duffing oscillator with mass disturbance were studied by Qiao [31,32]. The influences of system parameters on the response and stability of the variable mass oscillator differ from those of the system without variable mass.…”

Stationary Response of a Kind of Nonlinear Stochastic Systems with Variable Mass and Fractional Derivative Damping

“…Consider the following single-degree-of-freedom nonlinear stochastic system [19] with a variable mass and a fractional derivative damping,…”

“…Wang et al [18] utilized Gaussian white noise to describe the random mass disturbance and proposed the stochastic averaging technique of the variable mass system based on Hamilton theory, which provided a method to analyze the random responses of stochastic systems with Gaussian-white-noise-based variable mass. Then, Qiao et al [19,20] presented a group of stochastic stability conditions of the variable mass system under the Gaussian white noise excitation by using the stochastic averaging method and the maximum Lyapunov exponent method. Li [21] analyzed the stochastic response of a vibro-impact system with variable mass under the Gaussian white noise excitation, as well as its stochastic P-bifurcation characteristics.…”