Self-organization of weighted networks for optimal synchronizability

Optimal network design for synchronization of coupled oscillators

“…Various metrics have been proposed in the literature to quantify and optimize the synchronization performance. A broad class of these metrics focuses on the transient response, such as the ability of the network to resynchronize after perturbations (Donetti et al, 2005;Motter et al, 2005;Pecora and Carroll, 1998;Kempton et al, 2015). In this context, synchronizability can be characterized by either the required effort to synchronize the network (Sjödin et al, 2014), the speed of convergence to the synchronization manifold (Xiao and Boyd, 2004;Fardad et al, 2014b), or the range of coupling values for which a network with uniform coupling strengths would synchronize (Pecora and Carroll, 1998).…”

“…Using the master stability framework, proposed in (Pecora and Carroll, 1998), it was shown that the Laplacian algebraic connectivity and the Laplacian eigenratio are two network-dependent measures able to capture the synchronizability of a network of identical coupled oscillators. Based on this connection, we find in the literature several works aiming to optimize the synchronizability of a network of identical coupled oscillators using the Laplacian matrix (Pecora and Carroll, 1998;Nishikawa and Motter, 2006;Donetti et al, 2005;Rad et al, 2008;Motter et al, 2005Motter et al, , 2013Kempton et al, 2015;Skardal and Arenas, 2015;Fardad et al, 2014a;Clark et al, 2014;Mousavi et al, 2016;Siami and Motee, 2016).…”