Explosive death in direct and indirectly coupled oscillators: Review

Abstract

Abstract The transition in the dynamical behavior in the coupled system has several applications in science. The phase transitions of synchronization and oscillation suppression have both been thoroughly researched for a very long time. The second-order transition, which is continuous and reversible, is demonstrated by the standard results in the vast majority of cases in the coupled system. Recently, the first-order transitions reported in oscillation suppression have been reported in the complex network of the coupled oscillators through direct and indirect interaction. Explosive death is a transition that is not only abrupt but also irreversible in its parameters. We currently have a very good grasp of first order transition in oscillation death in networked systems and a variety of significant contributions and advancements have substantially improved it. Here, we aim to provide a review on the explosive death in various direct and indirect coupled oscillator scenarios while reviewing the previous findings.