Multistability in a system of two coupled oscillators with delayed feedback.

Highlights • Asymptotics of relaxation solutions of DDE with large parameter is built. • Studying of dynamics of DDE is reduced to studying dynamics of special mapping. • Coexisting of stable relaxation periodic solutions is shown. Abstract In this paper, nonlocal dynamics of a system of two differential equations with a compactly supported nonlinearity and delay is studied. For some set of initial conditions asymptotics of solutions of considered system is constructed. By this asymptotics we build a special mapping. Dynamics of this mapping describes dynamics of initial system in general: it is proved that stable cycles of this mapping correspond to exponentially orbitally stable relaxation periodic solutions of initial system of delay differential equations. It is shown that amplitude, period of solutions of initial system, and number of coexisting stable solutions depend crucially on coupling parameter. Algorithm for constructing many coexisting stable solutions is described. [ABSTRACT FROM AUTHOR]