A new hybrid learning law, the differential competitive law, which uses the neuronal signal velocity as a local unsupervised reinforcement mechanism, is introduced, and its coding and stability behavior in feedforward and feedback networks is examined. This analysis is facilitated by the recent Gluck-Parker pulse-coding interpretation of signal functions in differential Hebbian learning systems. The second-order behavior of RABAM (random adaptive bidirectional associative memory) Brownian-diffusion systems is summarized by the RABAM noise suppression theorem: the mean-squared activation and synaptic velocities decrease exponentially quickly to their lower bounds, the instantaneous noise variances driving the system. This result is extended to the RABAM annealing model, which provides a unified framework from which to analyze Geman-Hwang combinatorial optimization dynamical systems and continuous Boltzmann machine learning.