Emergence of amplitude death scenario in a network of oscillators under repulsive delay interaction

We report the existence of amplitude death in a network of identical oscillators under repulsive mean coupling. Amplitude death appears in a globally coupled network of identical oscillators with instantaneous repulsive mean coupling only when the number of oscillators is more than two. We further investigate that, amplitude death may emerge even in two coupled oscillators as well as network of oscillators if we introduce delay time in the repulsive mean coupling. We have analytically derived the region of amplitude death island and find out how strength of delay controls the death regime in two coupled or a large network of coupled oscillators. We have verified our results on network of delayed Mackey-Glass systems where parameters are set in hyperchaotic regime. We have also tested our coupling approach in two paradigmatic limit cycle oscillators: Stuart-Landau and Van der Pol oscillators.