Fanni Selley (BME Budapest):
Coupled map systems with a continuum of sites.
Abstract: Coupled map systems are simple models of a finite or infinite network of interacting units. The dynamics is given by the composition of the (typically chaotic) individual dynamics and a coupling map representing the characteristics of the interaction. The coupling map usually includes a parameter 0 ? epsilon ? 1, representing the strength of interaction. The main interest in such models lies in the emergence of bifurcations when epsilon is varied. We initiate a new point of view which represents the state of the system as a distribution, allowing the investigation of a continuum of interacting units. We previously showed for a simple setup that two distinct limit behaviours exist: when epsilon is small, an initial distribution with sufficiently low variation tends to uniform distribution. On the other hand, for sufficiently large values of epsilon, an initial distribution with small support tends to a point mass. In this talk we report on our new results extending these results to more general coupled map systems.