Coexistence of exponentially many chaotic spin-glass attractors

Abstract

A chaotic network of size $N$ with delayed interactions which resembles a pseudo-inverse associative memory neural network is investigated. For a load $\alpha=P/N<1$, where $P$ stands for the number of stored patterns, the chaotic network functions as an associative memory of 2P attractors with macroscopic basin of attractions which decrease with $\alpha$. At finite $\alpha$, a chaotic spin glass phase exists, where the number of distinct chaotic attractors scales exponentially with $N$. Each attractor is characterized by a coexistence of chaotic behavior and freezing of each one of the $N$ chaotic units or freezing with respect to the $P$ patterns. Results are supported by large scale simulations of networks composed of Bernoulli map units and Mackey-Glass time delay differential equations.