Frequency synchronization facilitated by frequency differences: Dynamics of coupled-oscillator systems with damaged elements

This study investigates the synchronization dynamics of coupled-oscillator systems in which some of the oscillators are damaged and lose their autonomous oscillations. The damaged elements are modeled using damped oscillators; thus, the system is composed of both limit-cycle oscillators and damped oscillators. In this system, as is commonly observed in conventional coupled limit-cycle oscillators, frequency synchronization among oscillators is destroyed when the difference between the natural frequencies of the oscillators increases. However, in the presence of damped oscillators, frequency synchronization can be facilitated by further increasing the frequency difference from the desynchronization state. We conduct numerical simulations on coupled Stuart-Landau oscillators and investigate this reentrance of frequency synchronization systematically. We also propose an approximate theory to predict the stability of the synchronization state based on a linear stability analysis of the fixed point, which reveals the appearance of the Hopf modes. Using this theory, we argue that the reentrance of frequency synchronization driven by increasing frequency differences can be observed in a wide range of coupled-oscillator systems with damaged elements.