  The role of a new form of dynamic interaction is explored in a network of
generic identical oscillators. The proposed design of dynamic coupling
facilitates the onset of a plethora of asymptotic states including synchronous
states, amplitude death states, oscillation death states, a mixed state
(complete synchronized cluster and small amplitude unsynchronized domain), and
bistable states (coexistence of two attractors). The dynamical transitions from
the oscillatory to death state are characterized using an average temporal
interaction approximation, which agrees with the numerical results in temporal
interaction. A first-order phase transition behavior may change into a
second-order transition in spatial dynamic interaction solely depending on the
choice of initial conditions in the bistable regime. However, this possible
abrupt first-order like transition is completely non-existent in the case of
temporal dynamic interaction. Besides the study on periodic Stuart-Landau
systems, we present results for paradigmatic chaotic model of R\"ossler
oscillators and Mac-arthur ecological model.
