Adaptive synchronization in delay-coupled networks of Stuart-Landau oscillators

TL;DR

This paper introduces an adaptive algorithm using the speed-gradient method to automatically tune the coupling phase in delay-coupled Stuart-Landau oscillator networks, enabling control over various synchronized states.

Contribution

It develops a novel adaptive control method for selecting synchronization states in delay-coupled oscillator networks based on the speed-gradient approach.

Findings

The algorithm successfully switches between in-phase, splay, and cluster states.

Goal functions based on oscillator differences and order parameters are effective.

Adaptive tuning enables control over multistable synchronization regimes.

Abstract

We consider networks of delay-coupled Stuart-Landau oscillators. In these systems, the coupling phase has been found to be a crucial control parameter. By proper choice of this parameter one can switch between different synchronous oscillatory states of the network. Applying the speed-gradient method, we derive an adaptive algorithm for an automatic adjustment of the coupling phase such that a desired state can be selected from an otherwise multistable regime. We propose goal functions based on both the difference of the oscillators and a generalized order parameter and demonstrate that the speed-gradient method allows one to find appropriate coupling phases with which different states of synchronization, e.g., in-phase oscillation, splay or various cluster states, can be selected.