Signature of glassy dynamics in dynamic modes decompositions

Abstract

Glasses are traditionally characterized by their rugged landscape of disordered low-energy states and their slow relaxation towards thermodynamic equilibrium. Far from equilibrium, dynamical forms of glassy behavior with anomalous algebraic relaxation have also been noted, for example, in networks of coupled oscillators. Due to their disordered and high-dimensional nature, such systems have been difficult to study theoretically, but data-driven methods are emerging as a promising alternative that may aid in their analysis. Here, we characterize glassy dynamics using the dynamic mode decomposition, a data-driven spectral computation that approximates the Koopman spectrum. We show that the gap between oscillatory and decaying modes in the Koopman spectrum vanishes in systems exhibiting algebraic relaxation, and thus, we propose a model-agnostic signature for robustly detecting and analyzing glassy dynamics. We demonstrate the utility of our approach through both a minimal example of a one-dimensional ODE and a high-dimensional example of coupled oscillators.

4 page, 4 figures, plus supplement

References in corpus (18)

• A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition
• On Dynamic Mode Decomposition: Theory and Applications
• Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
• Applied Koopmanism
• Chaos as an Intermittently Forced Linear System
• Long Time Evolution of Phase Oscillator Systems
• Linking connectivity, dynamics and computations in low-rank recurrent neural networks
• On Convergence of Extended Dynamic Mode Decomposition to the Koopman Operator
• Isostables, isochrons, and Koopman spectrum for the action-angle representation of stable fixed point dynamics
• Transition to chaos in random neuronal networks
• Vortex Glass and Vortex Liquid in Oscillatory Media
• Chimera States in Continuous Media: Existence and Distinctness
• Volcano transition in a solvable model of oscillator glass
• Nature of the Volcano Transition in the Fully Disordered Kuramoto Model
• Detecting regime transitions in time series using dynamic mode decomposition
• Volcano transition in populations of phase oscillators with random nonreciprocal interactions
• Koopman analysis in oscillator synchronization
• Detection of Functional Communities in Networks of Randomly Coupled Oscillators Using the Dynamic-Mode Decomposition

Cited by in corpus (1)

• Dynamics and chaotic properties of the fully disordered Kuramoto model