Forthcoming events in this series


Tue, 15 Feb 2011
11:00
DH 3rd floor SR

On Optimisation

Jari Fowkes
(Mathematics (Oxford))
Tue, 01 Feb 2011
11:00
DH 3rd floor SR

Stochastic Parameterisation

Hannah Arnold
(AOPP (Oxford University))
Abstract

This will be a discussion on Stochastic Parameterisation, led by Hannah.

Thu, 18 Feb 2010
11:00
DH 3rd floor SR

Submarine Hunting and Other Applications of the Mathematics of Tracking. (NOTE Change of speaker and topic)

Trevor Wood
(Oxford)
Abstract

The background for the multitarget tracking problem is presented

along with a new framework for solution using the theory of random

finite sets. A range of applications are presented including

submarine tracking with active SONAR, classifying underwater entities

from audio signals and extracting cell trajectories from biological

data.

Thu, 04 Feb 2010
11:00
DH 3rd floor SR

Differential Geometry Applied to Dynamical Systems

Prof. Jean-Marc Ginoux
(France)
Abstract

This work aims to present a new approach called Flow Curvature Method

that applies Differential Geometry to Dynamical Systems. Hence, for a

trajectory curve, an integral of any n-dimensional dynamical system

as a curve in Euclidean n-space, the curvature of the trajectory or

the flow may be analytically computed. Then, the location of the

points where the curvature of the flow vanishes defines a manifold

called flow curvature manifold. Such a manifold being defined from

the time derivatives of the velocity vector field, contains

information about the dynamics of the system, hence identifying the

main features of the system such as fixed points and their stability,

local bifurcations of co-dimension one, centre manifold equation,

normal forms, linear invariant manifolds (straight lines, planes,

hyperplanes).

In the case of singularly perturbed systems or slow-fast dynamical

systems, the flow curvature manifold directly provides the slow

invariant manifold analytical equation associated with such systems.

Also, starting from the flow curvature manifold, it will be

demonstrated how to find again the corresponding dynamical system,

thus solving the inverse problem.

Moreover, the concept of curvature of trajectory curves applied to

classical dynamical systems such as Lorenz and Rossler models

enabled to highlight one-dimensional invariant sets, i.e. curves

connecting fixed points which are zero-dimensional invariant sets.

Such "connecting curves" provide information about the structure of

the attractors and may be interpreted as the skeleton of these

attractors. Many examples are given in dimension three and more.