arXiv subjects

Peter E. Kloeden

Publications and source records attributed to Peter E. Kloeden.

21 records · Page 2Linked to original sources

arXiv2009

Synchronization of dissipative dynamical systems driven by non-Gaussian Levy noises

Dynamical systems driven by Gaussian noises have been considered extensively in modeling, simulation and theory. However, complex systems in engineering and science are often subject to non-Gaussian fluctuations or uncertainties. A coupled dynamical system under non- Gaussian Levy noises is considered. After discussing cocycle prop- erty, stationary orbits and random attractors, a synchronization phe- nomenon is shown to occur, when the drift terms of the coupled system satisfy certain dissipativity and integrability conditions. The synchro- nization result implies that coupled dynamical systems share a dy- namical feature in some asymptotic sense.

math.DS↗

arXiv2004

Exponential Stability Of The Quasigeostrophic Equation Under Random Perturbations

he 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 forcing, random boundary conditions, viscosity, Ekman constant and Coriolis parameter, all quasigeostrophic motion approach a unique stationary state exponentially fast. This stationary state corresponds to a unique invariant Dirac measure

math.AP↗

arXiv1999

Dissipative Quasigeostrophic Motion under Temporally Almost Periodic Forcing

The full nonlinear dissipative quasigeostrophic model is shown to have a unique temporally almost periodic solution when the wind forcing is temporally almost periodic under suitable constraints on the spatial square-integral of the wind forcing and the $β$ parameter, Ekman number, viscosity and the domain size. The proof involves the pullback attractor for the associated nonautonomous dynamical system.

chao-dyn↗