Out-of-phase mixed-mode oscillations of two strongly coupled identical relaxation oscillators

Abstract

We analyzed bifurcations of periodic regimes generated in the systems of two identical relaxation oscillators under strong coupling through a ``slow'' (inhibitory) variable. It was numerically shown that complex spatiotemporal behavior is observed near the boundaries of stability of the known antiphase periodic attractor and inhomogeneous steady states. Specifically, the following attractors were found: (i) a set of cycles of the antiphase type, each of which consists of one full-amplitude excursion and of the different number of small-amplitude high-frequency oscillations (the period of antiphase mixed-mode regimes is much greater than that of simple antiphase oscillations), (ii) inhomogeneous regimes of the above described type (out-of-phase mixed mode) with unequal numbers of small oscillations for different oscillators, (iii) period doubling cascades of the out-of-phase mixed mode that lead to the appearance of chaotic attractors. We showed that the modes found are not specific for our particular model; however, they are common for several classes of models and sensitive to the stiffness of oscillators. We discuss also conditions for the generation of such regimes. \textcopyright{} 1996 The American Physical Society.