On Duffing equation with random perturbations

On Lyapunov Control of the Duffing Equation

This brief addresses the robust asymptotic and BIB0(bounded-input bounded-output) stability of a class of linear shift-variant multidimensional systems. Using a shift-invariant comparisonsystem, necessary and sufficient conditions for the stability of the entirefamily of systems are derived.

Nonresonant Excitation of the Forced Duffing Equation

We investigate the hard nonresonant excitation of the forced Duffing equation with a positive damping parameter E. Using the symbolic manipulation system MACSYMA, a computer algebra system. we derive the two term perturbation expansion by the method of multiple time scales. The resulting approximate solution is valid for small values of the coefficient e As the damping parameter e increases, th...

Exponential Stability of the Quasigeostrophic Equation under Random Perturbations

Progress in Probability 49(2001), 241-256. The quasigeostrophic model describes large scale and relatively slow fluid motion in geophysical flows. We investigate the quasigeostrophic model under random forcing and random boundary conditions. We first transform the model into a partial differential equation with random coefficients. Then we show that, under suitable conditions on the random forc...

On the Dirichlet problem for a Duffing type equation

Recently the classical variational problem for a Duffing type equation received again some attention. In [1], [2], [7], some variational approaches were used in order to receive the existence of solutions for both periodic and Dirichlet type boundary value problems. Mainly direct method is applied under various conditions pertaining to at most quadratic growth imposed on the nonlinear term give...

Existence of Periodic Solutions for the Duffing Equation with Impulses