  We develop a framework in which the activity of nonlinear pulse-coupled
oscillators is posed within the renewal theory. In this approach, the evolution
of inter-event density allows for a self-consistent calculation that determines
the asynchronous state and its stability. This framework, can readily be
extended to the analysis of systems with more state variables. To exhibit this,
we study a nonlinear pulse-coupled system, where couplings are dynamic and
activity dependent. We investigate stability of this system and we show it
undergoes a super-critical Hopf bifurcation to collective synchronization.
