The resistive states of long Josephson junctions (LJJ) with strong fri
ction are studied numerically. Besides a variety of chaotic behaviours
different types of attractors are found for LJJs driven by dc bias cu
rrent. We use a model based on the damped sine-Gordon equation (SGE) a
nd assume that the influence of the bias field is felt through the bou
ndary conditions only. The zero-field steps in the current-voltage cha
racteristics and fine spatial structure of the time-averaged supercurr
ent density are discussed.