First-order phase transitions in the Kuramoto model with compact bimodal frequency distributions

Abstract

The Kuramoto model of a network of coupled phase oscillators exhibits a first-order phase transition when the distribution of natural frequencies has a finite flat region at its maximum. First-order phase transitions including hysteresis and bistability are also present if the frequency distribution of a single network is bimodal. In this study we are interested in the interplay of these two configurations and analyze the Kuramoto model with compact bimodal frequency distributions in the continuum limit. As of yet, a rigorous analytic treatment has been elusive. By combining Kuramoto's self-consistency approach, Crawford's symmetry considerations, and exploiting the Ott-Antonsen ansatz applied to a family of rational distribution functions that converge towards the compact distribution, we derive a full bifurcation diagram for the system's order parameter dynamics. We show that the route to synchronization always passes through a standing wave regime when the bimodal distribution is compounded by two unimodal distributions with compact support. This is in contrast to a possible transition across a region of bistability when the two compounding unimodal distributions have infinite support.

16 pages, 11 figures

References in corpus (14)

• Synchronization in complex networks
• Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
• Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators
• Explosive synchronization in adaptive and multilayer networks
• Exact Results for the Kuramoto Model with a Bimodal Frequency Distribution
• Thermodynamic limit of the first-order phase transition in the Kuramoto model
• Connecting the Kuramoto Model and the Chimera State
• Correlations, fluctuations and stability of a finite-size network of coupled oscillators
• Time delay in the Kuramoto model with bimodal frequency distribution
• A model bridging chimera state and explosive synchronization
• Transition to Collective Oscillations in Finite Kuramoto Ensembles
• Low Dimensional Dynamics of the Kuramoto Model with Rational Frequency Distributions
• Coupled networks and networks with bimodal frequency distributions are equivalent
• Finite Size Scaling in the Kuramoto Model

Cited by in corpus (12)

• Non-reciprocal phase transitions
• Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: a review
• Exact finite-dimensional description for networks of globally coupled spiking neurons
• Kuramoto model for populations of quadratic integrate-and-fire neurons with chemical and electrical coupling
• Collective dynamics of phase-repulsive oscillators solves graph coloring problem
• First-order like phase transition induced by quenched coupling disorder
• Complexified Synchrony
• A Two-Frequency-Two-Coupling model of coupled oscillators
• Critical exponents in coupled phase-oscillator models on small-world networks
• Classification of bifurcation diagrams in coupled phase-oscillator models with asymmetric natural frequency distributions
• Chimeras with uniformly distributed heterogeneity: two coupled populations
• Efficient moment-based approach to the simulation of infinitely many heterogeneous phase oscillators