Three-state network design for robust loop-searching systems

Neural network model for path-finding problems with the self-recovery property

The large-scale synchronization of neural oscillations is crucial in the functional integration of brain modules, but the combination of modules changes depending on the task. A mathematical description of this flexibility is a key to elucidating the mechanism of such spontaneous neural activity. We present a model that finds the loop structure of a network whose nodes are connected by unidirectional links. Using this model, we propose a path-finding system that spontaneously finds a path connecting two specified nodes. The solution path is represented by phase-synchronized oscillatory solutions. The model has the self-recovery property: that is, it is a system with the ability to find a new path when one of the connections in the existing path is suddenly removed. We show that the model construction procedure is applicable to a wide class of nonlinear systems arising in chemical reactions and neural networks.

Study of the neural dynamics for understanding communication in terms of complex hetero systems

The purpose of the research project was to establish a new research area named "neural information science for communication" by elucidating its neural mechanism. The research was performed in collaboration with applied mathematicians in complex-systems science and experimental researchers in neuroscience. The project included measurements of brain activity during communication with or without languages and analyses performed with the help of extended theories for dynamical systems and stochastic systems. The communication paradigm was extended to the interactions between human and human, human and animal, human and robot, human and materials, and even animal and animal.

Multistate network model for the pathfinding problem with a self-recovery property

In this study, we propose a continuous model for a pathfinding system. 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 a stable solution of the proposed model. The system has a self-recovery property, i.e., the system can find a path when one of the connections in the existing path is suddenly terminated. Further, we demonstrate that the appropriate installation of inhibitory interaction improves the search time.

Multistate network for loop searching system with self-recovery property

We propose a network of excitable systems that spontaneously initiates and completes loop searching against the removal and attachment of connection links. Network nodes are excitable systems of the FitzHugh-Nagumo type that have three equilibrium states depending on input from other nodes. The attractors of this network are stationary solutions that form loops, except in the case of an acyclic network. Thus, the system is regarded as a loop searching system. To design a system capable of self-recovery (the ability to find a loop when one of the connections in an existing loop is suddenly removed), we have investigated regulatory rules for the interaction between nodes and have used two characteristic properties of nonlinear dynamical systems to provide a solution: postinhibitory rebound phenomena and saddle-node bifurcation.