Sync: Persistence in Two Diffusively Coupled Oscillators
  We address the problem of stability of synchronization in two diffu- sively coupled oscillators under small perturations. We have two cases, namely, when the perturation becomes of a linear operator and the case of non-linear operator. We use the Lyapunov second method to guar- antee the global analysis for the first case. For the second, we use the Hartman-Grobman theorem, providing local analysis. 
Marcos D. N. Maia, Tiago Pereira
math.DS