Inferring topologies of complex dynamical networks with stochastic perturbations and coupling delay

In this paper, topology inference of complex dynamical networks with coupling delay and stochastic perturbations is considered. Based on the LaSalle-type theorems for stochastic differential delay equations, an adaptive estimation strategy is proposed to infer the underlying topology of a general delayed complex dynamical network by constructing an auxiliary network. It is worth noting that the unknown network model contains practical stochastic perturbations, and noisy node dynamics is taken as control input of the constructed auxiliary network. Numerical simulations will provide to verify the effectiveness of the proposed method.