Application of reconstructed phase-space techniques for correlation-dimension calculations in a spatially extended dynamical system

Abstract

The correlation dimension is calculated for data from a partial-differential-equation model of a magnetic-domain wall---the Bloch wall in a magnetic thin film. The data were extracted from different locations along the height of the wall and two types of embedding were used: a time-delay method from data taken at a single location in the wall (reconstructed phase space) and data taken from ten locations in the wall simultaneously (physical phase space). Three chaotic attractors of the Bloch wall were studied. The time-delay method for some attractors gives a dependence of the correlation dimension on the location at which the data were extracted. This dependence has a specific symmetry with respect to the film in which the Bloch wall resides and a surface (or boundary) effect is seen---the correlation dimension is different at the surfaces of the film. Several scaling regions are found in some cases. The physical phase-space embedding yields a correlation dimension which is an average of the spatial dependence obtained in the time-delay method, but usually this embedding gives a somewhat lower value of the correlation dimension.