We analyzed bifurcations of periodic regimes generated in the systems of two identical relaxation oscillators under strong coupling through a ''slow'' ͑inhibitory͒ 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: ͑i͒ a set of cycles of the antiphase type, each of which consists of one full-amplitude excursion and of the different number of smallamplitude high-frequency oscillations ͑the period of antiphase mixed-mode regimes is much greater than that of simple antiphase oscillations͒, ͑ii͒ inhomogeneous regimes of the above described type ͑out-of-phase mixed mode͒ with unequal numbers of small oscillations for different oscillators, ͑iii͒ 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. ͓S1063-651X͑96͒06806-7͔
A two-parametrical bifurcation analysis of the dynamics of two identical asymmetrically coupled Brusselators is performed disregarding limitations on the coupling strength and on the parameter choice with respect to Hopf bifurcation. The bifurcations of inhomogeneous steady states and periodic attractors are calculated as functions of the coupling strength and one of the free parameters. Inherent bifurcations for all kinds of solutions and relationships between attractors are established. A four-dimensional scenario of the infinite period bifurcation was considered. Special attention is paid to the spatially inhomogeneous limit cycle which can occupy a large window in a parameter space. It is shown that the structure of the phase diagram is strongly affected by the stiffness, which is a typical feature of real oscillators. The role of the fast variable exchange in the existence of inhomogeneous regimes is discussed.
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