Abstract
An array of Bloch walls (all with the same handedness) in a spatially periodic field is modelled by a chain of particles with finite mass (Doering mass of the Bloch walls) in an external periodic potential. Between two neighbouring Bloch walls there acts a repulsive exponentially decreasing interaction. Systems with one open and one fixed end are investigated. The stationary states are spatially chaotic solutions of a two-dimensional area-preserving map. Moving the fixed Bloch wall into the direction of the open end generates also temporal chaos. For very slow motion an erratic sequence of avalanches of all sizes occurs. This self-organized criticality disappears for large damping.