Analysis of the Asynchronous State in Networks of Strongly Coupled Oscillators

A general method is presented for the analysis of the asynchronous state in networks of identical, all-to-all coupled, limit-cycle oscillators of arbitrary dimension and with arbitrarily strong coupling. It is shown that, with strong coupling, this state can be destabilized in directions orthogonal to the limit cycle, which may change the units' behavior qualitatively. An example, involving integrate and fire neurons with spike adaptation, exhibits a bifurcation to a synchronized bursting state for strong feedback coupling. The analysis can account for transitions that cannot be studied in the commonly used phase-coupled approximation.