Convergence analysis of a class of simplified background neural networks with two subnetworks

Motivated by Salinas's (2003) original discovery in [1] and inspired by Oja's (1982) seminal work in [2], in this paper, we propose a class of simplified background neural networks model with two subnetworks. Some basic dynamic properties including boundedness, global attractivity, stability, and complete convergence are analyzed rigorously. The main contributions in this paper are as follows: (1) The boundedness of the new model is verified and conditions for global attractivity are derived. (2) Conditions on asymptotically stable of equilibrium points are obtained. (3) Complete convergence for the new network is proved by constructing a novel energy function. Finally, numerical examples demonstrate our theoretical results.