Stabilizing weighted complex networks

Abstract

Real networks often consist of local units which interact with each other via asymmetric and heterogeneous connections. In this paper, the V-stability problem is investigated for a class of asymmetric weighted coupled networks with nonidentical node dynamics, which includes the unweighted network as a special case. Pinning control is suggested to stabilize such a coupled network. The complicated stabilization problem is reduced to measuring the semi-negative property of the characteristic matrix which embodies not only the network topology, but also the node self-dynamics and the control gains. It is found that network stabilizability depends critically on the second largest eigenvalue of the characteristic matrix. The smaller the second largest eigenvalue is, the more the network is pinning controllable. Numerical simulations of two representative networks composed of non-chaotic systems and chaotic systems, respectively, are shown for illustration and verification.