It is well known that the current-driven point contact Josephson junctions exihibit the transition between periodic and chaotic states. The objective of this investigation is to study the behavior of this transition. In this work the RCSJ model has been used. The basic mechanism for the occurrence of this transition involves the variation of the parameter of the nonlinear system.In this system, various routes to chaos and the existence of the bistable state have been found. The phenomenon that the bistable state can transfer from periodic to the chaotic states at different values of the parameter is discussed.