Nonlinear system dynamics in the normalisation process of a self-organising neural network for combinatorial optimisation

Abstract

The weight normalisation process used for constraint satisfaction in a self-organising neural network (SONN) for combinatorial optimisation is investigated in this paper. The process relies on the mutual interaction of neuronal weights for computation, and we present a theoretical model to capture its longterm equilibrium dynamics. By solving the equilibrium states numerically, we reveal some nonlinear system phenomena hidden in the normalisation process: fixed point, symmetry-breaking bifurcation and cascades of period-doubling bifurcations to chaos. This leads to a new perspective of the weight normalisation within the SONN as a computational process based on nonlinear dynamics. © Springer..