ENERGY MINIMIZATION IN THE NONLINEAR DYNAMIC RECURRENT
*Rensselaer Polytechnic Institute, Cognitive science department, 110 Eighth Street,
Carnegie 108, Troy, NY 12180-3590 USA. Phone: 1 (518) 276-2692, Fax: 1 (518) 276-
3017, E-mail: firstname.lastname@example.org.
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 proven analytically. In the
present, 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.
Keywords: Artificial neural network, dynamical system, energy function, recurrent
associative memory, Cohen-Grossberg theorem.