Hysteresis in a generalized Kuramoto model with a first-order approximate coupling function and inhomogeneous coupling strengths

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 first-order approximation of general coupling functions. With the 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 first-order approximate coupling function and coupling strength inhomogeneity, suggesting the broad applicability of our findings to complex real-world systems.