Synchonization in Oscillator Networks with Heterogeneous Delays, Switching Topologies and Nonlinear Dynamics

This paper investigates the attractivity properties of the locked-in-phase equilibria set in oscillator networks, in the presence of multiple, non-commensurate communication delays. The dynamics that the oscillators are endowed with are in the form of nonlinear delay differential equations, with Kuramoto-type interactions. Using an appropriate LaSalle invariance principle we assess the attractivity properties of this set for arbitrary topology interconnections. We then show that this set is also asymptotically attracting even if the network topology is allowed to change