Traveling Waves of a Class of Simplified Background Neural Networks

Salinas proposed a class of background neural networks to analyze how the background controls the stability of the state. However, due to the complex network equation, some properties of the original network are difficult to be analyzed. Inspired by Oja's seminal work, in this paper, we propose a class of simplified background neural networks model with arbitrary exponents by using Taylor's theorem. Some contributions in this paper are as follows: (1) The nonuniform solution of the model is obtained when the connectivity is gaussian profile. (2) Traveling waves of the simplified model are analyzed with the connectivity profile that is slightly shifted when the background input is zero.In the end, an example is provided to show the proposed results.