Coexistence of exponentially many chaotic spin-glass attractors

TL;DR

This paper investigates a chaotic neural network with delayed interactions, revealing an exponential number of chaotic spin-glass attractors that coexist and depend on the network's load and size.

Contribution

It demonstrates the existence of exponentially many chaotic attractors in a delayed neural network, extending understanding of complex attractor landscapes in high-dimensional systems.

Findings

Number of attractors scales exponentially with network size

Chaotic attractors coexist with frozen states

Large-scale simulations support theoretical results

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.