Energy minimization in the nonlinear dynamic recurrent associative memory

Chartier and his colleagues have recently proposed a nonlinear synchronous attractor neural network. In the Nonlinear Dynamic Recurrent Associative Memory (NDRAM), learning has been shown to converge to a set of real-valued attractors in single-layered neural networks and bidirectional associative memories. However, the transmission is highly nonlinear and its global stability has never been analytically proven. In this article, it is shown that NDRAM is an instance of the Cohen-Grossberg class of models and its energy function is defined. Analysis of the energy function shows that the transmission is stable in the entire domain of NDRAM. Numerical simulations further support this analysis.