Widening Lock Range in Mutually Synchronized Oscillators With Multistability

ABSTRACT Multistability emerges in mutually synchronized oscillator systems. In the case of two reactively coupled oscillators, multiple coexisting modes appear, each exhibiting a different self‐sustained oscillation phase difference. Since these modes correspond to distinct oscillation frequencies, injection locking with an external signal, whose frequency falls within the system's bandwidth, is theoretically possible, with each mode having a finite lock range. If the amplitude of the external signal is sufficiently large, the lock ranges of different modes can overlap, effectively expanding the overall lock range. In this study, we consider a mutually synchronized system consisting of identically structured tunnel diode oscillators coupled via capacitive elements. We perform a bifurcation analysis of an injection locking system where each oscillator receives an external signal with individually controlled phase. Our results reveal that when the phase difference of the external signals is set to zero, only the in‐phase synchronization mode exhibits a finite lock range, while setting it to results in a finite lock range for the anti‐phase mode alone. Furthermore, by optimizing the phase difference of the external signals, the lock ranges of both modes can be overlapped, thereby achieving broadband synchronization.