Greedy optimization for growing spatially embedded oscillatory networks

TL;DR

This paper introduces a greedy algorithm for growing spatially embedded oscillator networks that enhances stability while minimizing link length costs, with implications for network resilience and efficiency.

Contribution

The paper presents a novel greedy growth algorithm that optimizes stability and topological properties of spatial oscillator networks, extending to heterogeneous networks.

Findings

Network stability improves with the algorithm under certain parameters.

Resulting networks have approximately exponential degree distributions.

Topological parameters related to resilience and efficiency are affected.

Abstract

The coupling of some types of oscillators requires the mediation of a physical link between them, rendering the distance between oscillators a critical factor to achieve synchronization. In this paper we propose and explore a greedy algorithm to grow spatially embedded oscillator networks. The algorithm is constructed in such a way that nodes are sequentially added seeking to minimize the cost of the added links' length and optimize the linear stability of the growing network. We show that, for appropriate parameters, the stability of the resulting network, measured in terms of the dynamics of small perturbations and the correlation length of the disturbances, can be significantly improved with a minimal added length cost. In addition, we analyze numerically the topological properties of the resulting networks and find that, while being more stable, their degree distribution is approximately exponential and independent of the algorithm parameters. Moreover, we find that other topological parameters related with network resilience and efficiency are also affected by the proposed algorithm. Finally, we extend our findings to more general classes of networks with different sources of heterogeneity. Our results are a first step in the development of algorithms for the directed growth of oscillatory networks with desirable stability, dynamical and topological properties.