Dynamical phase transitions in short-ranged and long-ranged neural network models
K. E. Kürten · Journal de physique · 1989
The period of limit cycles, the time evolution of the distance between two initial configurations and the local activity distribution are compared in finite- and infinite dimension threshold automata. The Hamming distance criterium, well established as a powerful tool for the localization of critical parameters, is complemented by criteria incorporating quantities as the average length of the cyclic modes as well as the local activity distribution which both can distinguish between two phases : an ordered phase and a chaotic phase. Due to their strongly correlated spatial structure short-ranged lattice models exhibit by far more ordered behavior than their infinite-range counterparts.