Generation of Synchronous Unpredictable Oscillations by Coupled Hopfield Neural Networks

TL;DR

This paper introduces a criterion based on generalized synchronization to generate unpredictable oscillations in coupled Hopfield neural networks, supported by simulations and analysis of synchronization measures.

Contribution

It extends the concept of unpredictable oscillations to coupled Hopfield neural networks using a new synchronization-based criterion.

Findings

Unpredictable oscillations can be generated in coupled HNNs.

Generalized synchronization ensures the transfer of unpredictability.

Simulations confirm the theoretical predictions.

Abstract

A new criterion based on generalized synchronization is provided for the extension of unpredictable oscillations among coupled Hopfield neural networks (HNNs). It is shown that if a drive HNN possesses an unpredictable oscillation, then a response HNN also possesses such an oscillation provided that they are synchronized in the generalized sense. Extension of unpredictability in coupled 4D HNNs are exemplified with simulations. The auxiliary system approach and conditional Lyapunov exponents are utilized to demonstrate the presence of synchronization.