Reduced phase space analysis for hysteretic oscillators of masing type

Hysteretic oscillators can be represented as dynamic systems provided a high dimension phase space is considered. It is shown that for a fairly large class of oscillators, based on Masing rules, the dynamics can be studied over a two-dimensional manifold. Theoretical motivations and algorithms are presented. Developed procedures are tested on two simple but important oscillators, one of them has an unstable branch and is the hysteretic counterpart of the Duffing one-wells two-bumps oscillator. Though the applications mainly have the scope to illustrate the way the procedures of solution work, some aspects of the dynamic response are investigated in depth. In particular it is shown that the well-known sequence: breaking of symmetry-cascade of period doubling, does not appear in practice in the two bumps hysteretic oscillator. Subharmonic oscillations are observed throughout.