This paper describes a construction mechanism of group behavior on decentralized autonomous robotic systems with cooperation. The decentralized autonomous robotic systems refer to multiple robotic systems including many autonomous robots, such as the cellular robotic system (CEBOT). The CEBOT consists of a number of functional robotic units called "cells". In the research on the CEBOT, same as the decentralized robotic systems, it is one of the most important issues to cooperate among many robots for the group behavior and to coordinate the group behavior, since it is important to organize the behavior of each robot in the multiple robotic systems. In order to organize the behavior in dynamic environment, we proposed a concept of the "self-recognition" for the decision making of the behavior in a robotic group. In addition to the proposed concept, this paper shows the construction mechanism of group behavior using the character of attractor. Based on this idea, we present the behavioral evolution of the group robotic systems.