6 documents found

Article / Chapter
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2006-07-07

Measure Attractors and Markov Attractors

The actions induced by a random dynamical system on spaces of probability measures on the state space are investigated, and generalisations of the notion of an attractor are discussed and compared. For the particular case of a random dynamical system generated by a stochastic differential equation the...
Article / Chapter
2006-03-07

Stabilization of linear systems by dynamic high-gain rotation

We discuss stabilisation of linear systems by dynamic high-gainrotation. The existence of stabilizing rotations is established forsystems with negative trace, and an adaptive method to choose thecontroller gain is presented. The stabilization is robust with respectto arbitrary (possibly time-varying)...
Article / Chapter
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2005-11-25

Stabilization of linear systems by rotation

We introduce the concept of `stabilization by rotation' for deterministic linear systems with negative trace. This concept encompasses the well known concept of "vibrational stabilization" introduced by Meerkov in the 1970s and is a deterministic version of 'stabilization by noise' for stochastic systems...
Article / Chapter
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2005-10-17

The effect of noise on the Chaffee-Infante Equation : a nonlinear case study

We investigate the effect of perturbing the Chafee-Infante scalar reaction diffusion equation, ut - [Delta]u = [beta]u - u3, by noise. While a single multiplicative Itô noise of sufficient intensity will stabilise the origin, its Stratonovich counterpart leaves the dimension of the attractor essentially...
Article / Chapter
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2004-05-04

Towards a Morse theory for random dynamical systems

A generalization of the concepts of deterministic Morse theory to random dynamical systems is presented. Using the notions of attraction and repulsion in probability, the main building blocks of Morse theory such as attractor-repeller sets, Morse sets, and the Morse decomposition are obtained for random...