On practical synchronisation and collective behaviour of networked heterogeneous oscillators*

We present preliminary results on synchronisation of nonlinear oscillators interconnected in heterogeneous networks that is, we assume that the systems’ dynamic models are different, albeit of the same dimension. Under mild conditions, we show that the synchronisation errors may be diminished by increasing the interconnection gain. That is, we establish results on practical synchronisation. Although this problem has been studied in the literature, our approach is novel from an analytical perspective: the behaviour of the interconnected systems is determined by two main components, the stability of an averaged dynamics, relative to an attractor of what we call emergent dynamics and, secondly, the synchronisation of each individual oscillator relative to the emergent dynamics. Our framework is general, it covers as a particular case that of (set-point) consensus but also trajectory-tracking synchronisation and consensus over manifolds.