Research on oscillation quenching of coupled Landau–Stuart systems based on positive–negative coupling

Oscillation quenching is a common and widely studied dynamical phenomenon in coupled nonlinear systems, primarily including Amplitude Death (AD) and Oscillation Death (OD). This paper investigated the effects of positive–negative coupling on oscillation quenching in coupled Landau–Stuart systems, with a particular focus on AD and OD. Through the linear stability analysis of fixed points and numerical calculations, it was found that in coupled identical systems, when the coupling rate α<0.0152, the system easily exhibited OD without any AD. Conversely, it transitioned directly to the Oscillation State (OS) for α≥0.0152, which indicated that negative coupling (α<0) drove the system into OD and expanded the OD regions, whereas positive coupling (α>0) made it easier to OS directly. However, in coupled non-identical systems, the introduction of negative coupling also drove the system toward OD, expanding the OD regions and reducing the AD regions, while positive coupling had the opposite effects. Moreover, compared to the case without positive–negative coupling, the system could more readily achieve mutual transitions among OD, AD, and OS through appropriate adjustments of the coupling parameters. This study contributed to a deeper understanding of AD and OD phenomena and provided new possibilities for better controlling such systems.