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In this talk, we first consider a simple model of two coupled phase oscillators, where stable phase-locking emerges when the coupling strength is sufficiently large. We then consider two diffusively coupled Stuart-Landau oscillators. To investigate oscillatory dynamics from a mathematical perspective, we transform the coupled system into polar coordinates and analyze the existence and stability of phase-locked solutions. We begin by examining the symmetric and asymmetric coupling cases separately. Finally, we adopt a bifurcation viewpoint to unify these cases and illustrate the transition from symmetric to asymmetric coupling regimes through bifurcation diagrams of phase-locked solutions.

More information: https://scholar.google.com/citations?user=M_K6uN0AAAAJ&hl=zh-TW