On the chaotic oscillations of Bloch walls and their control

In this paper elements of chaos theory are applied to the study of the dynamics of a model for a 180 ° Bloch wall under the action of an alternating magnetic field. Only the case of soft ferromagnetic materials without nonferromagnetic inclusions is considered. The necessary tools for the numerical investigation of the possible unstable oscillations of such a system in the chaos domain of the control parameter are elaborated. This investigation implied the stabilisation of the oscillations by an adapted OGY parametric method, in which a control parameter proportional to the fieldʹs amplitude was chosen. The study of the periodic orbits extracted from the chaotic attractor regards the dissipation on these orbits, which is compared to the power losses during the uncontrolled chaotic oscillations and with those in the periodicity range of the control parameter. The conclusion is that periodic orbits with power losses smaller than those of the other two types can be found.