  We study chaotic behavior of order parameters in two coupled ensembles of
self-sustained oscillators. Coupling within each of these ensembles is switched
on and off alternately, while the mutual interaction between these two
subsystems is arranged through quadratic nonlinear coupling. We show
numerically that in the course of alternating Kuramoto transitions to synchrony
and back to asynchrony, the exchange of excitations between two subpopulations
proceeds in such a way that their collective phases are governed by an
expanding circle map similar to the Bernoulli map. We perform the Lyapunov
analysis of the dynamics and discuss finite-size effects.
