Explosive and semi-explosive death in coupled oscillators

In this paper, we propose a new kind of transition process from oscillation to death state that is different from the traditional explosive death called semi-explosive death. In this process, two kinds of death arise in different ways. We investigate the occurrence of semi-explosive death transition for the first time on globally conjugate-coupled Van der Pol (VdP) oscillators with asymmetry factor. Semi-explosive death is an irreversible transition of half first order and half second order. That is, this process not only happens with an abrupt, irreversible transition that is a common feature of first order phase transition, but also includes a continuous second order change. Moreover, the forward and the backward second order transition points for this transition have been obtained theoretically, which is in complete agreement with the numerical results. Finally, the details of the transition mechanisms between semi-explosive death and explosive death along with dependence of asymmetry factor and damping coefficient are also discussed theoretically and numerically.