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An experimental arrangement and a set of experiments are developed to generate empirical evidence of the effect of noise on a rotating, macro-scale cantilever structure. The experiment is a controlled representation of a rotating machinery blade. Due to the nature of the nonlinear restoring forces acting on the cantilever structure, the structure's response includes regions of multi-stability and hysteresis. Here, a large number of trials are used to show that random perturbations can be used to create a transition between a high amplitude response and a low amplitude response of the cantilever. The observed transition behavior occurs from a high amplitude response to a low amplitude response, but not vice versa. Stochastic modeling of the system, Monte Carlo simulations, and calculations of the stochastic system's quasipotential are used to explain the nearly one-directional transition behavior. These noise-influenced transitions can also occur in other physical systems. • Construction of an experimental setup to study stochastic dynamics of a rotating beam. • Measurements of noise-induced transitions from high- to low-amplitude responses. • Quasipotential analysis and Monte Carlo simulations of noise-induced transitions. [ABSTRACT FROM AUTHOR]

Abstract Nongradient stochastic differential equations (SDEs) with position-dependent and anisotropic diffusion are often used in biological modeling. The quasi-potential is a crucial function in the Large Deviation Theory that allows one to estimate transition rates between attractors of the corresponding ordinary differential equation and find the maximum likelihood transition paths. Unfortunately, the quasi-potential can rarely be found analytically. It is defined as the solution to a certain action minimization problem. In this work, the recently introduced Ordered Line Integral Method (OLIM) is extended for computing the quasi-potential for 2D SDEs with anisotropic and position-dependent diffusion scaled by a small parameter on a regular rectangular mesh. The presented solver employs the dynamical programming principle. At each step, a local action minimization problem is solved using straight line path segments and the midpoint quadrature rule. The solver is tested on two examples where analytic formulas for the quasi-potential are available. The dependence of the computational error on the mesh size, the update factor K (a key parameter of OLIMs), as well as the degree and the orientation of anisotropy is established. The effect of anisotropy on the quasi-potential and the maximum likelihood paths is demonstrated on the Maier–Stein model. The proposed solver is applied to find the quasi-potential and the maximum likelihood transition paths in a model of the genetic switch in Lambda Phage between the lysogenic state where the phage reproduces inside the infected cell without killing it, and the lytic state where the phage destroys the infected cell. Graphical abstract Highlights • Computation of the quasi-potential for SDEs with multiplicative noise on a mesh. • An experimental study of the numerical error on two test examples. • An application to the Maier–Stein model with anisotropic diffusion. • An application to the Aurell and Sneppen SDE for a genetic switch in Lambda Phage. [ABSTRACT FROM AUTHOR]