Heterogeneity induced splay state of amplitude envelope in globally coupled oscillators

Splay states of the amplitude envelope are stably observed as a heterogenous node is introduced into the globally coupled identical oscillators with repulsive coupling. With the increment of the frequency mismatches between the heterogenous nodes and the rest identical globally coupled oscillators, the formal stable splay state based on the time series becomes unstable, while a splay state based on the new-born amplitude envelopes of time series is stably observed among the rest identical oscillators. The characteristics of the splay state based on the amplitude envelope are numerically and theoretically presented for different parameters of the coupling strength [Formula: see text] and the frequency mismatches [Formula: see text] for small coupling strength and large frequency mismatches. We expect that all these results could reveal the generality of splay states in coupled nonidentical oscillators and help to understand the rich dynamics of amplitude envelopes in multidisciplinary fields.