Nonlinear Phenomena in Hysteretic Systems

This paper discusses the different transitions from periodicity to quasi-periodicity, intermittency and chaos in systems with hysteresis. Three types of hysteresis are considered: the Bouc-Wen law of hysteresis, the Masing law and the pseudoelastic constitutive law typical of shape memory alloys. The first two rate-independent models do not account for heat transfers, while in the third case the thermodynamic transformations are taken into account. It is shown that these systems share similar trends for the loss of stability of the fundamental response to highly nonlinear responses of various kinds.