Bifurcations and chaotic oscillations in an automatic control relay systemwith hysteresis

The dynamics of relay system with hysteresis is investigated. Systems of th is type have a broad range of applications for power control and temperatur e regulation or in order to obtain highly stabilized electric or magnetic f ields. Examples are power supplies for radio-electronics, computer equipmen t or spacecrafts, test stands for investigations of high- or low-temperatur e superconductivity, electron microscopes, and nuclear magnetic resonance t omographs. We first describe a general approach to determine stable and uns table periodic orbits for systems with hysteresis. Considering a concrete e xample of a four-dimensional relay system with hysteresis we hereafter dete rmine the regions of periodic and chaotic oscillations in parameter space. The regularities in the occurrence of periodic motions are studied, and the associated bifurcations are described. The causes of nondeterminate (i.e. chaotic) dynamics are discussed and the influence of an external noise sign al is analyzed.