Local analysis of phase transitions in networks with varying connection strengths

It has been observed in networks with rapidly varying connection strengths that individual node activation levels can grow explosively in a phase where total network activation remains bounded. On the basis of the results reported by F. McFadden et al. (1991), the authors extend the previous research to apply to a more general class of connectionist models, and they identify additional phase transition boundaries not covered by previous research. Sufficient conditions are derived for boundedness of the activation vector of the system, not only for total activation. In addition, sufficient conditions are derived for divergence in the absence of external input. The mathematical results are illustrated by computer simulation results using a competitive activation model, and the simulations are used for exploration of the phase space