Effects of spatial frequency distributions on amplitude death in an array of coupled Landau-Stuart oscillators

The influences of spatial frequency distributions on complete amplitude death are explored by studying an array of diffusively coupled oscillators. We found that with all possible sets of spatial frequency distributions, the two critical coupling strengths εc1 (lower-bounded value) and εc2 (upper-bounded value) needed to get complete amplitude death exhibit a universal power law and a log-normal distribution respectively, which has long tails in both cases. This is significant for dynamics control, since large variations of εc1 and εc2 are possible for some spatial arrangements. Moreover, we explore optimal spatial distributions with the smallest (largest) εc1 or εc2.