Abstract
Our purpose is to complete the analysis of a class of hybrid dynamical systems with autonomous switchings generated by a hysteresis phenomenon. Because we yet have found limit period-1 cycles in paper (Quémard et al, 2005b) and because we deal with nonlinear equations systems, the question of the existence of more than one solution for them and so of the existence of cycles with more than one period is rather natural. Equations system for period-2 cycles is determined and a notion of stability is studied. A realistic application to a thermostat with anticipative resistance comes to illustrate theoretical results.
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