Dimensional collapse and fractal attractors of a system with fluctuating delay times

A frequently encountered situation in the study of delay systems is that the length of the delay time changes with time, which is of relevance in many fields such as optics, mechanical machining, biology or physiology. A characteristic feature of such systems is that the dimension of the system dynamics collapses due to the fluctuations of delay times. In consequence, the support of the long-trajectory attractors of this kind of systems is found being fractal in contrast to the fuzzy attractors in most random systems.