Observation of positive Lyapunov exponent induced by gain increase of neuron nonlinearity in complex-valued associative memories

A positive Lyapunov exponent is observed in complex-valued associative memories having dynamical attractors, when a small-signal gain of neuron nonlinearity is increased. When the gain is small, the Lyapunov exponent is constantly zero (normal behaviour). However, it is found in the experiment that, unlike conventional (real-valued) associative memories, the Lyapunov exponent becomes distinctly positive (chaotic behaviour) for a larger neuron gain even if the weighting factors are unchanged. This result suggests that the gain of nonlinear devices has a critical significance on information processing stability in future coherent neural networks