Synchronization of coupled nonidentical dynamical systems

We analyze the stability of synchronized state for coupled nearly identical dynamical systems on networks by deriving an approximate master stability function (MSF). Using this MSF we treat the problem of designing a network having the best synchronizability properties. We find that the edges which connect nodes with a larger relative parameter mismatch are preferred. Also, the nodes having values at one extreme of the parameter mismatch are preferred as hubs where the extreme is the one which gives a better stability according to the MSF curve.