Bifurcation analysis in a hybrid time delay system

In this paper, the rigorous analysis is presented for the bifurcation phenomena of a hybrid system containing time delay. First, we introduce a simple system and its behavior of the orbit, and derive a return map explicitly. The fundamental bifurcation phenomenon is analyzed by using one and two parameter bifurcation diagrams. Even in a simple system containing delay time, we discover the two stable orbits coexist, m-piece chaotic attractor, and so on. Finally, we consider the fundamental differences between ideal and time delay system.