Dynamics of Minimal Networks: Ring of Oscillators*

Several natural and engineering systems exhibiting oscillatory behavior can be modeled as minimal networks of oscillators. In such systems, oscillators that may not be direct neighbors can interact with distance-dependent time delays, resulting in local, nonlocal, or global coupling schemes. The present study examines how different coupling schemes and coupling parameters (number of oscillators, coupling strength, and time delay) affect the dynamics of a minimal ring of Stuart-Landau oscillators. As the coupling scheme changes from local to nonlocal, the variety of splay states and the region of amplitude death increases. Additionally, when all oscillators are coupled, a weak chimera state is observed when the delays are distance-dependent, whereas, generalized splay states are observed when the delays are identical. We anticipate that the insights from this study will help identify the underlying coupling scheme in thermo-fluid and other physical systems.