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.)