Self-recovery of function is one of the remarkable properties of biological systems and its implementation in autonomous distributed systems is highly desirable. In this study focusing on designing logical connections by using dynamical systems, we propose an autonomous distributed system which is capable of searching for closed loops. A closed loop is defined as a phase synchronization of a group of oscillators belonging to the corresponding nodes. We demonstrate that the system can find a possible loop when one of the connections in the existing loop is suddenly removed.