Three-state network design for robust loop-searching systems

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, we propose an autonomous distributed system which is capable of searching for closed loops in a network in which nodes are connected by unidirectional paths. A closed loop is defined as a phase synchronization of a group of oscillators belonging to the corresponding nodes. In addition, to develop a system capable of self-recovery (the ability to find a loop when one of the connections in the existing loop is suddenly removed), we have developed regulatory rules for the interaction between nodes. These rules are used to construct a regulation network in which the stability of nodes and that of loops are mutually sustained, allowing the system to function as a loop-searching system with self-recovery properties.