Continuous model for pathfinding system with self-recovery property

This study propose a continuous pathfinding system based on coupled oscillator systems. We consider acyclic graphs whose vertices are connected by unidirectional edges. The proposed model autonomously finds a path connecting two specified vertices, and the path is represented by phase-synchronized oscillatory solutions. To develop a system capable of self-recovery, that is, a system with the ability to find a path when one of the connections in the existing path is suddenly removed, we implemented three-state Boolean-like regulatory rules for interaction functions. We also demonstrate that appropriate installation of inhibitory interaction improves the finding time.