Stable normal-mode vibrations in engineering can be undesirable and one of the possibilities for quenching these is by embedding the oscillator in an autoparametric system by coupling to a damped oscillator. There exists the possibility of destabilizing the undesirable vibrations by a suitable tuning and choice of nonlinear coupling parameters. An additional feature is that, to make the quenchi...

Time evolution of the expectation values of various dynamical operators of the harmonic oscillator with dissipation is analitically obtained within the framework of the Lindblad theory for open quantum systems. We deduce the density matrix of the damped harmonic oscillator from the solution of the Fokker-Planck equation for the coherent state representation, obtained from the master equation fo...

The history of the linear time-delayed and time-periodic oscillator demonstrates how stability theory has developed from the damped oscillator to the delayed Mathieu equation. Based on these results, it is a natural idea to apply time-periodic control gains when large time delay in the feedback loop tends to destabilize the system. By formulating the act-and-wait control concept as a special ca...

It is demonstrated that the general theory of Casimir and van der Waals forces describes interaction-induced equilibrium thermodynamic potentials damped harmonic oscillator bilinearly coupled to environment. An extended model for a suggested along lines forces, corresponding quantities obtained. While original involves heat bath consisting large number free oscillators having infinitesimal damp...

We apply a semi-discrete in time relaxation scheme to a weakly damped forced nonlinear Schrödinger system. This provides us with a discrete infinite-dimensional dynamical system. We prove the existence of a global attractor for this dynamical system.

The interdecadal variability of a stochastically forced four-box model of the oceanic meridional thermohaline circulation (THC) is described and compared to the THC variability in the coupled ocean-atmosphere GCM of Delworth, Manabe, and Stouffer (1993). The box model is placed in a linearly stable thermally dominant mean state under mixed boundary conditions. A linear stability analysis of thi...