Splay States in a Ring of Coupled Oscillators: From Local to Global Coupling

In this work, we study dynamical behavior in a ring of coupled nonlinear oscillators and focus on the stability of homogeneous steady state and splay states by performing linear stability analysis. Different cases from local (nearest-neighbor) coupling to global (all-to-all) coupling by increasing the range of coupling are studied. Some explicit stability results for each possible splay state are analytically obtained. It is valuable to compare their similarities and differences for these different cases. All these results could shed improved light on our understanding of the organization of splay states in coupled oscillators.