Storing Cycles in Hopfield-type Networks with Pseudoinverse Learning Rule - Retrievability and Bifurcation Analysis

Abstract

In this paper, we study retrievability of admissible cycles and the dynamics of the networks constructed from admissible cycles with the pseudoinverse learning rule. Retrievability of admissible cycles in networks with $C_0>0$ and $λ$ sufficiently large are discussed. Based on the linear stability analysis we derive a complete description of all possible local bifurcations of the trivial solution for the networks constructed from admissible cycles. We illustrate numerically that, depending on the structural features, the admissible cycles are respectively stored and retrieved as attracting limit cycles, unstable periodic solutions and delay-induced long-lasting transient oscillations, and the transition from fixed points to the attracting limit cycle bifurcating from the trivial solution takes place through multiple saddle-nodes on limit cycle bifurcations.