QMUL coordinates MANMADE, the EU network on "Diagnosing vulnerability, emergent phenomena, and volatility in man-made networks". Workpackage 3 develops methods to analyse the topology and dynamics of networks (joint with H. Touchette and D.K. Arrowsmith)
Joint project with H. Kantz and G. Radons.
Joint project with H. Benner.
Parts of my previous research were performed within a program of the Sonderforschungsbereich 185. Some details about the project:
In the last few years one has gained tremendous insight into the properties of dynamical systems with few relevant degrees of freedom. One concept which has proven to be fruitful in this field is the approach by symbolic dynamics and the application of statistical methods. These concepts relate the description of dynamical systems with the statistical mechanics of spin chains. Bifurcations in low dimensional chaotic systems and the corresponding singular local structures can be characterized successfully in terms of phase transitions. By way of contrast less is known about the influence of chaotic dynamics on the evolution of spatially extended systems with a large number of degrees of freedom. Systems of coupled maps provide a suitable class of models to study this issue. The application of thermodynamic concepts yields a description in terms of two dimensional spin lattices. The ergodic properties, especially the occurrence of exponentially long transients and the coexistence of a large number of stable states can be investigated. It seems promising to describe the pattern formation as an equilibrium phase transition in the associated spin lattice and to identify critical behaviour.