THE LENGTH OF ATTRACTORS IN ASYMMETRIC RANDOM NEURAL NETWORKS WITH DETERMINISTIC DYNAMICS

I have developed a method to detect attractors of any length in large neural networks with up to 1024 neurons within a reasonable period of CPU time. In networks with symmetric couplings only stable states and, in the case of parallel dynamics, cycles of length 2 exist. The presented simulations suggest that, in sufficiently large systems, this holds also for couplings up to a distinct value of asymmetry. Beyond this value extremely long cycles are detected and the average cycle length depends exponentially on system size.