Dynamic stability analysis of a class of recurrent neural networks with uniform firing rate

This paper studies the dynamic stability properties of 1-D nonlinear neural networks with uniform firing rate. By employing Taylor's theorem, a class of recurrent neural networks model with uniform firing rates is proposed, in which multiple equilibria can coexist. The contributions of this paper are: (1) An invariant set of 1-D neural networks is expressed by explicit inequality and boundedness is proved. (2) Complete stability is studied via constructing a novel energy function. (3) Examples and simulation results are illustrated to validate our theories.