Sushchestvovanie edinstvennoy nepodvizhnoy tochki otobrazheniy, porozhdennykh mnogomernoy sistemoy s releynym gisterezisom

Abstract

A multidimensional system of ordinary differential equations with relay hysteresis is considered. The system parameters are assumed to be such that there exists a family of continuous operators each of which maps some connected compact set into itself. In this case, the operator corresponds to a periodic orbit with an even number of switching points in the phase space of the system. For the operator family, a necessary and sufficient condition for the existence of a single fixed point is obtained.