Applied Dynamical Systems Seminar (past)
|
Tue, 27/11/2007 10:00 |
Dr. Reason Machete |
Applied Dynamical Systems Seminar  |
DH 3rd floor SR |
|
Tue, 13/11/2007 10:00 |
Dr. Max Little |
Applied Dynamical Systems Seminar |
DH 3rd floor SR |
| Many biological time series appear nonlinear or chaotic, and from biomechanical principles we can explain these empirical observations. For this reason, methods from nonlinear time series analysis have become important tools to characterise these systems. Nonetheless, a very large proportion of these signals appear to contain significant noise. This randomness cannot be explained within the assumptions of pure deterministic nonlinearity, and, as such, is often treated as a nuisance to be ignored or otherwise mitigated. However, recent work points to this noise component containing valuable information. Random dynamical systems offer a unified framework within which to understand the interplay between deterministic and stochastic dynamical sources. This talk will discuss recent attempts to exploit this synthesis of stochastic and deterministic dynamics in biological signals. It will include a case study from speech science. | |||
|
Tue, 30/10/2007 10:00 |
Dr.Oscar Martinez-Alvarado |
Applied Dynamical Systems Seminar |
DH 3rd floor SR |
|
Sat, 13/10/2007 11:00 |
Laura Campbell |
Applied Dynamical Systems Seminar |
DH 3rd floor SR |
|
Tue, 07/11/2006 11:00 |
Xiaodong Luo (Oxford) |
Applied Dynamical Systems Seminar |
DH 3rd floor SR |
|
Tue, 29/11/2005 11:00 |
Prof Alexander Gorban (University of Leicester) |
Applied Dynamical Systems Seminar |
DH 3rd floor SR |
| The concept of the slow invariant manifold is the central idea underpinning a transition from micro to macro and model reduction in kinetic theories. We present the constructive methods of invariant manifolds for model reduction in physical and chemical kinetics, developed during last two decades. The physical problem of reduced description is studied in the most general form as a problem of constructing the slow invariant manifold. The invariance conditions are formulated as the differential equation for a manifold immersed in the phase space. The equation of motion for immersed manifolds is obtained. Invariant manifolds are fixed points for this equation, and slow invariant manifolds are Lyapunov stable fixed points, thus slowness is presented as stability. A collection of methods to derive analytically and to compute numerically the slow invariant manifolds is presented. The systematic use of thermodynamic structures and of the quasi-chemical representation allows us to construct approximations which are in concordance with physical restrictions. The following examples of applications are presented: Nonperturbative derivation of physically consistent hydrodynamics from the Boltzmann equation and from the reversible dynamics, for nudsen numbers Kn~1; construction of the moment equations for nonequilibrium media and their dynamical correction (instead of extension of the list of variables) in order to gain more accuracy in description of highly nonequilibrium flows; model reduction in chemical kinetics. | |||
|
Tue, 22/11/2005 16:30 |
Dr Hinke Osinga (University of Bristol) |
Applied Dynamical Systems Seminar |
Dobson Room, AOPP |
|
The Lorenz system still fascinates many people because of the simplicity of the
equations that generate such complicated dynamics on the famous butterfly
attractor. The organisation of the dynamics in the Lorenz system and also how
the dynamics depends on the system parameters has long been an object of study.
This talk addresses the role of the global stable and unstable manifolds in
organising the dynamics. More precisely, for the standard system parameters, the
origin has a two-dimensional stable manifold and the other two equilibria each
have a two-dimensional unstable manifold. The intersections of these two
manifolds in the three-dimensional phase space form heteroclinic connections
from the nontrivial equilibria to the origin. A parameter-dependent study of
these manifolds clarifies not only the creation of these heteroclinic
connections, but also helps to explain the dynamics on the attractor by means of
symbolic coding in a parameter-dependent way. This is joint work with Eusebius Doedel (Concordia University, Montreal) and Bernd Krauskopf (University of Bristol). |
|||
|
Tue, 15/11/2005 11:00 |
Dr Stefano Luzzatto |
Applied Dynamical Systems Seminar |
Imperial College |
| We formulate and prove a Jakobson-Benedicks-Carleson type theorem on the occurrence of nonuniform hyperbolicity (stochastic dynamics) in families of one-dimensional maps, based on computable starting conditions and providing explicit, computable, lower bounds for the measure of the set of selected parameters. As a first application of our results we obtain a first ever explicit lower bound for the set of parameters corresponding to maps in the quadratic family f_{a}(x) = x^{2}-a which have an absolutely continuous invariant probability measure. | |||
|
Tue, 01/11/2005 11:00 |
Prof Bernd Krauskopf (University of Bristol) |
Applied Dynamical Systems Seminar |
DH 3rd floor SR |
|
Tue, 18/10/2005 11:00 |
Oscar Martinez-Alvarado (Moderator) |
Applied Dynamical Systems Seminar |
DH 3rd floor SR |
