Explosive death induced by environmental coupling

In the real world, numerous biological and chemical systems reveal abundant and interesting dynamical behaviors due to the diversity of the ways in which elements interact with each other. Many recent studies have shown that an explosive transition can be found in different dynamical models. However, it is still unclear under which conditions will cause the onset of explosive transition. In this paper, the explosive phenomenon on a networked system where oscillators coupled mutually via a directly diffusion and a common indirectly environment related to every oscillator is reported. An expression of close connection among the system and the dynamic environments' decay rate as well as the intrinsic frequency of each subsystem is observed numerically. In particular, different decay rates could generate explosive death, semi-explosive death, and amplitude death states, respectively. Moreover, a small frequency can exhibit the typical second-order continuous transition from oscillation to death state, and an appropriate and sufficiently large frequency could be more common and more likely to induce the first-order transition. Following this, the theoretical analysis about the critical transition boundaries for different dynamic behaviors is established in such directly-indirectly coupled system for the first time. The results provide a new way for the control mechanism of explosive phenomenon, which is critical for further understanding the underlying patterns of the first-order phase transition on dynamic networked systems.