Stability of a ring of coupled van der Pol oscillators with non-uniform distribution of the coupling parameter

The stability of a ring of coupled van der Pol oscillators is studied in this work considering a non-uniform distribution of the coupling parameter along the ring. The stability analysis is based on the transformation of the linearized equation of the ring into a canonical Hill equation. A stability condition is derived considering the stability of the non-periodic term of the Hill equation. Stable and unstable dynamic behavior of the ring is studied by means of numerical simulations.