Synchronization of heterogeneous oscillators under network modifications: Perturbation and optimization of the synchrony alignment function

Abstract

Synchronization is central to many complex systems in engineering physics (e.g., the power-grid, Josephson junction circuits, and electro-chemical oscillators) and biology (e.g., neuronal, circadian, and cardiac rhythms). Despite these widespread applications---for which proper functionality depends sensitively on the extent of synchronization---there remains a lack of understanding for how systems evolve and adapt to enhance or inhibit synchronization. We study how network modifications affect the synchronization properties of network-coupled dynamical systems that have heterogeneous node dynamics (e.g., phase oscillators with non-identical frequencies), which is often the case for real-world systems. Our approach relies on a synchrony alignment function (SAF) that quantifies the interplay between heterogeneity of the network and of the oscillators and provides an objective measure for a system's ability to synchronize. We conduct a spectral perturbation analysis of the SAF for structural network modifications including the addition and removal of edges, which subsequently ranks the edges according to their importance to synchronization. Based on this analysis, we develop gradient-descent algorithms to efficiently solve optimization problems that aim to maximize phase synchronization via network modifications. We support these and other results with numerical experiments.

25 pages, 6 figures

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Cited by in corpus (9)

• Higher-order interactions improve optimal collective dynamics on networks
• Development of structural correlations and synchronization from adaptive rewiring in networks of Kuramoto oscillators
• Optimal phase synchronization in networks of phase-coherent chaotic oscillators
• Geometric unfolding of synchronization dynamics on networks
• Synchronization of Network-Coupled Oscillators with Uncertain Dynamics
• Multiplex Markov Chains: Convection Cycles and Optimality
• Grass-roots optimization of coupled oscillator networks
• Enhancement of Network Synchronizability via Two Oscillatory System
• Network-ensemble comparisons with stochastic rewiring and von Neumann entropy