A set of nonlinear differential equations that describe the dynamics of the ART1 model are presented, along with the motivation for their use. These equations are extensions of those developed by Carpenter and Grossberg (1987). It is shown how these differential equations allow the ART1 model to be realized as a collective nonlinear dynamical system. Specifically, we present an ART1-based neural network model whose description requires no external control features. That is, the dynamics of the model are completely determined by the set of coupled differential equations that comprise the model. It is shown analytically how the parameters of this model can be selected so as to guarantee a behavior equivalent to that of ART1 in both fast and slow learning scenarios. Simulations are performed in which the trajectories of node and weight activities are determined using numerical approximation techniques.
IEEE Transactions on Neural Networks
Chaos, Computer architecture, Differential equations
Abdallah, Chaouki T.; Gregory L. Heileman; and Michael Georgiopoulos. "A dynamical adaptive resonance architecture." IEEE Transactions on Neural Networks 5, 6 (1994): 873-889. doi:10.1109/72.329684.