# Optimizing stability of mutual synchronization between a pair of limit-cycle oscillators with weak cross coupling

## TL;DR

This paper develops a method to optimize the linear stability of synchronized states in weakly coupled limit-cycle oscillators by designing the coupling matrix, enhancing synchronization robustness.

## Contribution

It introduces a phase reduction-based approach to derive the optimal coupling matrix for maximizing stability under specific constraints.

## Key findings

- Optimal coupling matrices improve synchronization stability.
- The method applies to various types of limit-cycle oscillators.
- Enhanced stability demonstrated through numerical examples.

## Abstract

We consider optimization of linear stability of synchronized states between a pair of weakly coupled limit-cycle oscillators with cross coupling, where different components of state variables of the oscillators are allowed to interact. On the basis of the phase reduction theory, the coupling matrix between different components of the oscillator states that maximizes the linear stability of the synchronized state under given constraints on overall coupling intensity and on stationary phase difference is derived. The improvement in the linear stability is illustrated by using several types of limit-cycle oscillators as examples.