On controlling dynamic complex networks

Abstract

Controlling dynamic complex networks is challenging because constituent couplings are inherently nonlinear and nonstationary. Such properties can bring instability to network structure and render the collapse of emerging collective behaviors. Impact of disruptions such as random breakage of connection and permanent structural alteration caused by network constituents leaving or joining the network can be alleviated by adjusting constituent couplings. A multivariable nonlinear time–frequency network control scheme is presented in the general framework for complex networks [1] by which network dynamics and collective behaviors are described using information entropy and two time-variant degree-of-couplings (DOCs). Control is applied to network constituents to allow for the updating of DOCs in response to the dynamic state of the network delineated by information entropy. The control scheme is applied to mitigate a dynamic network of 20 constituents undergoing severed connections and arbitrary introduction of new constituents. The controller design is fast in response and robust in sustaining collective behaviors and network structure stability. Under the direction of the controller, network stability is attested by fewer adjustments to DOCs to meet the target information entropy. As a result, the time for the disturbed ensemble to reach synchronization is reduced and the stability and integrity of network structure are improved. Resilience of the network to various kinds of disruptions is positively correlated to the number of constituents to which control is applied.