Heterogeneous nucleation in finite size adaptive dynamical networks

Abstract

Phase transitions in equilibrium and nonequilibrium systems play a major role in the natural sciences. In dynamical networks, phase transitions organize qualitative changes in the collective behavior of coupled dynamical units. Adaptive dynamical networks feature a connectivity structure that changes over time, co-evolving with the nodes' dynamical state. In this Letter, we show the emergence of two distinct first-order nonequilibrium phase transitions in a finite size adaptive network of heterogeneous phase oscillators. Depending on the nature of defects in the internal frequency distribution, we observe either an abrupt single-step transition to full synchronization or a more gradual multi-step transition. This observation has a striking resemblance to heterogeneous nucleation. We develop a mean-field approach to study the interplay between adaptivity and nodal heterogeneity and describe the dynamics of multicluster states and their role in determining the character of the phase transition. Our work provides a theoretical framework for studying the interplay between adaptivity and nodal heterogeneity.

References in corpus (12)

• Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
• Adaptive Coevolutionary Networks: A Review
• Explosive Synchronization Transitions in Scale-free Networks
• Paths to Synchronization on Complex Networks
• Explosive synchronization in adaptive and multilayer networks
• Explosive transitions in complex networks' structure and dynamics: percolation and synchronization
• Thermodynamic limit of the first-order phase transition in the Kuramoto model
• The synchronized dynamics of time-varying networks
• Hysteretic transitions in the Kuramoto model with inertia
• Birth and stabilization of phase clusters by multiplexing of adaptive networks
• Model reduction for networks of coupled oscillators
• Transitions from trees to cycles in adaptive flow networks

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