In autonomous decentralized systems, it is expected that the overall
system functionality is maintained even when local failures occur, as
the constituent elements of the system behave appropriately. The
mathematical understanding of such self-recovery capabilities is crucial
not only in the context of life systems, such as the nervous system, but
also for comprehending the adaptability of environmental systems. In
this study, an attempt was made to elucidate the conditions necessary
for the self-recovery capabilities of autonomous decentralized systems
by constructing a specific dynamical model on a network.

As a specific task, the study explored the widely applicable pathfinding
problem in practical scenarios and developed a mathematical model with
the following properties:

(a) If a solution (a path connecting two given points under specified
boundary conditions) exists within the network, the exploration
continues until discovery is complete.
(b) After discovering a solution, if network disconnection or failures
occur, a new search for a solution is initiated.
(c) In cases where no solution exists, the computation is terminated
within a finite time.

Particularly, achieving property (c) requires ingenuity, and models
describing node dynamics incorporate phenomena such as post-inhibitory
rebound and SNIC bifurcation. The presentation introduces mathematical
models with properties satisfying (a) through (c) and discusses their
applicability to practical problems, such as robot arm control.

(This talk will be given in Japanese.)