In this talk we present a few recent results on regularity properties and numerical approximations for stochastic ordinary and partial differential equations with non-globally monotone nonlinearities. In particular, we establish strong convergence rates for Cox-Ingersoll-Ross (CIR) processes, stochastic Duffing-van der Pol oscillators, stochastic Lorenz equations, and Cahn-Hilliard-Cook equatio...

Container motion along a planar circular trajectory at constant angular velocity, i.e. orbital shaking, is of interest in several industrial applications, e.g. for fermentation processes or cultivation stem cells, where good mixing and efficient gas exchange are the main targets. Under these external forcing conditions, free surface typically exhibits primary steady-state through single-crest d...

The article considers an implicit finite-difference scheme for the Duffing equation with a derivative of fractional variable order Riemann–Liouville type. issues stability and convergence are considered. Test examples given to substantiate theoretical results. Using Runge rule, results compared explicit scheme. Phase trajectories oscillograms oscillator type constructed, chaotic modes detected ...

This work is focused on the numerical determination of Shannon probabilistic entropy for MEMS devices exhibiting some uncertainty in their structural response. a universal measure statistical or stochastic disorder static deformation dynamic vibrations engineering systems and available both continuous discrete distributions functions parameters. An interval algorithm using Monte Carlo simulatio...

Abstract In this study, we consider the experimentally obtained, periodically forced response of a nonlinear structure in presence process noise. Control-based continuation is used to measure both stable and unstable periodic solutions, while different levels noise are injected into system. Using these data, robustness control-based algorithm its ability capture noise-free system assessed by id...

By taking two-coupled duffing oscillator system as the research object, the study found under the synergistic effect of weak periodic signal and noise, the two-coupled duffing oscillator system has typical stochastic resonance and even could achieve better output of stochastic resonance than single duffing oscillator. Based on this phenomenon, this paper proposes a new method to detect the weak...

This paper discusses a novel technique and implementation to perform nonlinear control for two different forced model state oscillators and actuators. The paper starts by discussing the Duffing oscillator which features a second order non-linear differential equation describing complex motion whereas the second model is the Van der Pol oscillator with non-linear damping. A first order actuator ...

1 abstract We study equilibrium solutions for the problem u t = ε 2 u xx − u 3 + λu + cos x u x (0, t) = u x (1, t) = 0. Using a shooting method we find solutions for all non-zero ε. For small ε we add to the solutions found by previous authors, especially Angennent, Mallet-Paret and Peletier, and by Hale and Sakamoto, and also give new elementary ode proofs of their results. Among the new resu...