Memory selection and information switching in oscillator networks with higher-order interactions

TL;DR

This paper investigates how oscillator networks with higher-order interactions can store and switch between binary information states, identifying stable configurations and the conditions for state transitions.

Contribution

It introduces a stability criterion for memory states in higher-order oscillator networks and analyzes their capacity for information storage and switching.

Findings

Stable fixed points correspond to binary-like states representing information.

Network topology influences which states are stable.

The system can switch between stable states via perturbations.

Abstract

We study the dynamics of coupled oscillator networks with higher-order interactions and their ability to store information. In particular, the fixed points of these oscillator systems consist of two clusters of oscillators that become entrained at opposite phases, mapping easily to information more commonly represented by sequences of 0's and 1's. While $2^N$ such fixed point states exist in a system of $N$ oscillators, we find that a relatively small fraction of these are stable, as chosen by the network topology. To understand the memory selection of such oscillator networks, we derive a stability criterion to identify precisely which states are stable, i.e., which pieces of information are supported by the network. We also investigate the process by which the system can switch between different stable states when a random perturbation is applied that may force the system into the basin of attraction of another stable state.