Synchronization dynamics in non-normal networks: the trade-off for optimality

Abstract

Synchronization is an important behavior that characterizes many natural and human made systems composed by several interacting units. It can be found in a broad spectrum of applications, ranging from neuroscience to power-grids, to mention a few. Such systems synchronize because of the complex set of coupling they exhibit, the latter being modeled by complex networks. The dynamical behavior of the system and the topology of the underlying network are strongly intertwined, raising the question of the optimal architecture that makes synchronization robust. The Master Stability Function (MSF) has been proposed and extensively studied as a generic framework to tackle synchronization problems. Using this method, it has been shown that for a class of models, synchronization in strongly directed networks is robust to external perturbations. In this paper, our approach is to transform the non-autonomous system of coupled oscillators into an autonomous one, showing that previous results are model-independent. Recent findings indicate that many real-world networks are strongly directed, being potential candidates for optimal synchronization. Inspired by the fact that highly directed networks are also strongly non-normal, in this work, we address the matter of non-normality by pointing out that standard techniques, such as the MSF, may fail in predicting the stability of synchronized behavior. These results lead to a trade-off between non-normality and directedness that should be properly considered when designing an optimal network, enhancing the robustness of synchronization.

References in corpus (7)

• Synchronization in complex networks
• Synchronization is optimal in non-diagonalizable networks
• Topology-driven instabilities: the theory of pattern formation on directed networks
• Maximum Performance at Minimum Cost in Network Synchronization
• How limit cycles and quasi-cycles are related in systems with intrinsic noise
• Optimal phase synchronization in networks of phase-coherent chaotic oscillators
• Non-normality and non-monotonic dynamics in complex reaction networks

Cited by in corpus (17)

• Synchronization induced by directed higher-order interactions
• Turing patterns in systems with high-order interactions
• Turing patterns on discrete topologies: from networks to higher-order structures
• Broken detailed balance and entropy production in directed networks
• Non-reciprocal interactions enhance heterogeneity
• Persistence of chimera states and the challenge for synchronization in real-world networks
• Theory of phase reduction from hypergraphs to simplicial complexes: a general route to higher-order Kuramoto models
• Flutter Suppression Enhancement in Coupled Nonlinear Airfoils with Intermittent Mixed Interactions
• Dynamics in non-Hermitian systems with nonreciprocal coupling
• Revisiting weak values through non-normality
• Nonreciprocal amplification toward chaos in a chain of Duffing oscillators
• The Essential Synchronization Backbone Problem
• Pattern reconstruction through generalized eigenvectors on defective networks
• Hierarchical route to the emergence of leader nodes in real-world networks
• Network Hierarchy and Pattern Recovery in Directed Sparse Hopfield Networks
• Finite propagation enhances Turing patterns in reaction-diffusion networked systems
• Synchronization of nonlinearly coupled Stuart-Landau oscillators on networks