Synchrony as constraint
ABSTRACT :
We obtain necessary conditions for the {em generalised synchronization} of coupled dynamical systems, namely the process of confining the dynamics to lower dimensional submanifolds in the phase space. In this framework, synchronization is seen as a process of imposing algebraic constraints which may also be time-dependent. We propose a procedure for constructing (non-unique) coupling functions that can guide the flow to the desired submanifold which can also be made stable and attracting. A geometric analysis of the stability of this manifold is provided, and the procedure is demonstrated through representative examples.