Hysteresis in a Generalized Kuramoto Model with a Simplified Realistic Coupling Function and Inhomogeneous Coupling Strengths

TL;DR

This paper explores how inhomogeneous coupling strengths and a realistic coupling function induce hysteresis and abrupt phase transitions in a generalized Kuramoto model, with implications for complex systems like brain networks.

Contribution

It introduces a generalized Kuramoto model with inhomogeneous coupling and a simplified realistic coupling function, analyzing their effects on hysteresis and phase transitions.

Findings

Hysteresis occurs due to coupling strength inhomogeneity and realistic coupling functions.

Distribution of coupling strengths influences the hysteresis regions.

Hysteresis is observed in brain network models, indicating real-world relevance.

Abstract

We investigate hysteresis in a generalized Kuramoto model with identical oscillators, focusing on coupling strength inhomogeneity, which results in oscillators being coupled to others with varying strength, and a simplified, more realistic coupling function. With the more realistic coupling function and the coupling strength inhomogeneity, each oscillator acquires an effective intrinsic frequency proportional to its individual coupling strength. This is analogous to the positive coupling strength-frequency correlation introduced explicitly or implicitly in some previous models with nonidentical oscillators that show explosive synchronization and hysteresis. Through numerical simulations and analysis using truncated Gaussian, uniform, and truncated power-law coupling strength distributions, we observe that the system can exhibit abrupt phase transitions and hysteresis. The distribution of coupling strengths significantly affects the hysteresis regions within the parameter space of the coupling function. Additionally, numerical simulations of models with weighted networks including a brain network confirm the existence of hysteresis due to the realistic coupling function and coupling strength inhomogeneity, suggesting the broad applicability of our findings to complex real-world systems.