Dead zones and phase reduction of coupled oscillators

A dead zone in the interaction between two dynamical systems is a region of their joint phase space where one system insensitive to changes other. These can arise number contexts, and presence functions has interesting consequences for emergent dynamics. In this paper, we consider zones general coupled systems. For weakly limit cycle oscillators, investigate criteria that give rise functions. We applications multiscale oscillators coupling on only branch relaxation oscillation lead appearance description interaction.