Bifurcation from Synchrony in Homogeneous Networks

Abstract:

In this talk we discuss synchrony breaking bifurcations in regular networks. In the first part we study the consequences of a tensor product structure of the underlying equations. This structures allows to gain some insight into generic bifurcations. We compare various bifurcations results and their relevance for our problem.

In general it is rather difficult to obtain the precise form of the nonlinear terms in the bifurcation equations. We report on some recent attempts to overcome this problem in order to discuss generic behavior for C^∞ -systems using normal form theory.