Damage Propagation in a Diluted Asymmetric Neural Network

We study numerically the nature of the retrieval attractors in an asymmetrically diluted Hopfield neural network through the damage propagation technique. We consider the damage evolution of two replicas, initially very close to each other and having both finite projection with one memorized pattern. By analyzing the asymptotic behavior of the damage, we characterize the dynamical nature of the retrieval attractors. We found, in the recognition phase, a dynamical phase transition separating chaotic and fixed point retrieval trajectories. We also present a conjugate field h associated with the damage, which destroys the dynamical transition and whose corresponding susceptibility presents a sharp peak at the critical parameter.