We are moving to a system where all members of the blog can add news or make announcments about e.g. PhDs completed, upcoming workshops and conference etc. Watch this space!

We are moving to a system where all members of the blog can add news or make announcments about e.g. PhDs completed, upcoming workshops and conference etc. Watch this space! There will be a workshop at the University of Exeter on Tuesday 27th March 2012. There is no registration fee for this workshop but we would appreciate knowing if you will attend so we can organize catering. We thank the Royal Society for funding the visit of Dr Podvigina. Please let Asma Ismail or Peter Ashwin know if you want to attend or need more information. A provisional schedule is:
10.30-11.00 Martin Krupa (Paris/Exeter)
11.00-11.30 Jonathan Dawes (Bath)
11.30-12.00 Alexander Lohse (Hamburg) In my talk I will present recent results on the relationship between the stability index for heteroclinic cycles that Peter Ashwin and Olga Podvigina defined in their paper “On local attraction properties and a stability index for heteroclinic connections” and different stability properties of the cycle. The index quanties the extent of the basin of attraction of the cycle in a small ε-ball around it. It is related to stability properties of the cycle, but not always in an obvious way. For example, if there is a point on the cycle where the index exists and is greater than 0, then the cycle is essentially asymptotically stable (e.a.s.). A similar result can be shown for predominant asymptotic stability (p.a.s.) of the cycle in the case that the index exists everywhere and is greater than some constant c > 0. On the way to proving these results we establish a more general statement, namely that any cycle with a set of positive measure in its basin of attraction is e.a.s. One crucial idea for the proof of this was developed by Olga Podvigina. 12.10-13.30 lunch 13.30-14.10 Mike Field (Houston) We discuss a class of large adaptive networks of coupled discrete dynamical systems that relate to problems in computational neuroscience and learning (notably, Spike-Timing Dependent Plasticity or STDP). We describe some interesting examples of heteroclinic phenomena and cycling chaos that occur in these networks as well as some issues related to synchronous and asynchronous logic. We also show some preliminary work on SLOGALS logic (SLOppy Globally Asynchronous Locally Synchronous logic) that has implications for large asynchronous networks with significant random components. 14.10-14.40 Chris Bick (Goettingen) Dynamics and Bifurcations in Symmetric Phase Oscillator Systems” 14.40-15.30 Tea
16.05-16.55 Olga Podvigina (Moscow) Dynamical systems which are invariant under the action of a non-trivial symmetry group can possess structurally stable heteroclinic cycles. In this talk I discuss stability properties of a class of structurally stable heteroclinic cycles called heteroclinic cycles of type Z. It is well-known that a heteroclinic cycle that is not asymptotically stable can attract nevertheless a positive measure set from its small neighbourhood. I call such cycles fragmentarily asymptotically stable. Necessary and sufficient conditions for fragmentary asymptotic stability are expressed in terms of eigenvalues and eigenvectors of transition matrices. If all transverse eigenvalues of linearisations near steady states involved in the cycle are negative, then fragmentary asymptotic stability implies asymptotic stability. In the latter case the condition for asymptotic stability is that the transition matrices have an eigenvalue larger than one in absolute value. Finally, I discuss bifurcations occurring when the conditions for asymptotic stability or for fragmentary asymptotic stability are broken. Workshop Title: Location: Date: Programme: 10.00 – 11.00, Chris K.R.T. Jones “Sea-Ice as a Trigger of Thermohaline Oscillations and some thoughts on mathematics and climate” 11.00 – 11.20, David Stephenson “Mathematical modelling of weather and climate at Exeter: Overview of Exeter Climate Systems” 11.20 – 11.35 Tea break 11.35 – 11.55, Chris Ferro “Evaluating forecasting systems” 11.55 – 12.15, Renato Vitolo “Extreme value laws in chaotic dynamical systems” 12.15 – 12.35, Sebastian Wieczorek “On critical rates and triggers for tipping in forced systems” 12.35 – 14.00, Lunch break. Lunch has to be sorted out individually but we could all go to the Innovation Centre. 14.00 – 15.00, Jan Sieber “Application of timeseries analysis techniques to climate time series” 15.00 – 15.20, Matt Collins “Perspectives on Uncertain Climate Projections” 15.20 – 15.35 Tea break 15.35 – 15.55, Frank Kwasniok “Data-based stochastic subgrid parametrisation using cluster-weighted modelling” 15.55 – 16.15, John Thuburn “Using Differential Geometry to Develop Weather and Climate Models” 16.15 – 16.35, Peter Cox “Variability as a constraint on sensitivity: how likely is climate-driven tropical forest dieback?” For more details, please contact Sebastian Wieczorek. The rate of global warming could lead to a rapid release of carbon from peatlands that would further accelerate global warming. Two recent studies, including one that involves Centre members highlights the risk that this ‘compost bomb’ instability could pose, and calculate the rate-dependent conditions under which it could occur. http://www.exeter.ac.uk/news/featurednews/title,115755,en.html |