Identification of system parameters and network topology of delay-coupled complex networks under circumstance noise

Noting that the random noise and time delay are prevalent in complex networks and the topology of a network is often unknown or partially unknown, based on the principle of random generalized projective lag synchronization, an approach was proposed to estimate the system parameters and topological structure of delay-coupled complex networks under circumstance noise. By constructing an appropriate controller and adaptive updating rules, the unknown network parameters and topological structure of the concerned networks were identified simultaneously. The accuracy of the method was rigorously proved by the LaSalle-type theorem for stochastic differential delay equations. An example of network with chaotic oscillator was provided to illustrate the method. The numerical results indicate that the unknown network parameters and topological structure can be accurately identified, and yet the proposed method is robust against the time delay, the update gain and the network topology.