Complex Systems

Stochastic Stability of Nonsymmetric Threshold Networks Download PDF

Bronislaw Jakubczyk
Institute of Mathematics, Polish Academy of Sciences,
00-950 Warsaw, Sniadeckich 8, Poland


For a nonsymmetric threshold network equipped with an asynchronous dynamics, we show that if the product of weights in any cycle of units is nonnegative, then each trajectory converges to a stable state with probability one. We also show that such networks have a natural feed-forward layer structure and stability is achieved in a hierarchical order due to this structure. It follows then that this new class of networks can perform similar tasks as symmetric networks as well as new tasks due to its relation to directed graphs.