Reduced-order adaptive synchronization in a chaotic neural network with parameter mismatch: A dynamical system vs. machine learning approach

TL;DR

This paper compares a Lyapunov-based control method and a machine learning-based reservoir computing approach for synchronizing chaotic neural networks of different orders, demonstrating effectiveness through simulations.

Contribution

It introduces a novel combination of reservoir computing algorithms for adaptive synchronization of chaotic neural networks with parameter mismatch.

Findings

Lyapunov control successfully synchronizes 4D and 5D chaotic neurons.

Reservoir computing-based control effectively achieves synchronization.

The methods inspire future data-driven approaches for chaotic neural network control.

Abstract

In this paper, we address the reduced-order synchronization problem between two chaotic memristive Hindmarsh-Rose (HR) neurons of different orders using two distinct methods. The first method employs the Lyapunov active control technique. Through this technique, we develop appropriate control functions to synchronize a 4D chaotic HR neuron (response system) with the canonical projection of a 5D chaotic HR neuron (drive system). Numerical simulations are provided to demonstrate the effectiveness of this approach. The second method is data-driven and leverages a machine learning-based control technique. Our technique utilizes an ad hoc combination of reservoir computing (RC) algorithms, incorporating reservoir observer (RO), online control (OC), and online predictive control (OPC) algorithms. We anticipate our effective heuristic RC adaptive control algorithm to guide the development of more formally structured and systematic, data-driven RC control approaches to chaotic synchronization problems, and to inspire more data-driven neuromorphic methods for controlling and achieving synchronization in chaotic neural networks in vivo.