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DY: Fachverband Dynamik und Statistische Physik

DY 17: Nonlinear Dynamics I

DY 17.1: Topical Talk

Mittwoch, 16. März 2011, 10:15–10:45, ZEU 255

Nonlinear Dynamics of Complex Hysteretic Systems — •Günter Radons — Institute for Physics, Chemnitz University of Technology, D-09107 Chemnitz.

Under the influence of external fields a large variety of materials and systems shows very complex hysteretic behavior. The latter means that in addition to major hysteresis loops, one finds many subloops or minor loops. Well-known examples range from the magnetization of magnetic materials and the deformation of shape memory alloys to capillary condensation in porous materials. Such a behavior is traditionally described by so-called hysteresis operators [1]. Correspondingly, the interaction of such hysteretic systems with its environment is naturally described by operator-differential equations. Despite its importance and its ubiquitous appearance, the dynamics resulting from such equations is not well understood.

In this talk I will review the working principles of the Preisach hysteresis operator and its applications. Subsequently recent results on dynamical systems with such hysteretic subsystems will be presented. They range from the appearance of 1/f-noise under simple input-output conditions [2] to the co-existence of infinitely many attractors for operator-difference equations or operator-differential equations describing e.g. the motion of an iron sphere in an inhomogeneous magnetic field.

[1] G. Bertotti, I.D. Mayergoyz (Eds.), The Science of Hysteresis, Vol. I-III, Elsevier, 2006. [2] G. Radons, Phys. Rev. Lett. 100, 240602 (2008), Phys. Rev E 77, 061133 (2008), Phys. Rev E 77, 061134 (2008).