  Most previous studies on coupled dynamical systems assume that all
interactions between oscillators take place uniformly in time, but in reality,
this does not necessarily reflect the usual scenario. The heterogeneity in the
timings of such interactions strongly influences the dynamical processes. Here,
we introduce a time-evolving state-space dependent coupling among an ensemble
of identical coupled oscillators, where individual units are interacting only
when the mean state of the system lies within a certain proximity of the phase
space. They interact globally with mean-field diffusive coupling in a certain
vicinity and behave like uncoupled oscillators with self-feedback in the
remaining complementary subspace. Interestingly due to this occasional
interaction, we find that the system shows an abrupt explosive transition from
oscillatory to death state. Further, in the explosive death transitions, the
oscillatory state and the death state coexist over a range of coupling
strengths near the transition point. We explore our claim using Van der pol,
FitzHughNagumo and Lorenz oscillators with dynamic mean field interaction. The
dynamic interaction mechanism can explain sudden suppression of oscillations
and concurrence of oscillatory and steady state in biological as well as
technical systems.
