Organization

A01 | Mathematical Systems Theory

In the research subfield 'A01', the underlying mechanism of neural dynamics on communications is elucidated by the studies on evolutional systems, random dynamic systems, hybrid systems, and extended dynamic systems.

Group G1

TITLE
Creative processes of information in the dynamic brain and a functional role of chaotic itinerancy
OBJECT
By the recent development of measurement techniques which has been applied to the measurements of the states of brain, it has become possible to experimentally justify a dynamic theory of the brain, a part of which was proposed by our group from the aspect of chaotic dynamical systems. Actually, both the attractor dynamics and the transitory dynamics between attractor ruins have been found in the rat hippocampal slices including CA1 and CA3 regions, and also in the rabitt and rat olfactory bulb and olfactory cortices in many groups, inparticular, in Freeman's group. Furthermore, recent experimental findings strongly suggest the presence of selective processes of input information by top-down signals, that may be interpreted in terms of chaotic itinerancy that Ikeda, Kaneko and Tsuda proposed about twenty years ago. We also predicted the appearance of chaotic itinerancy in hippocampal CA3 and the realization of Cantor coding in CA1. This prediction on the Cantor coding was verified in CA1, using the rat hippocampal slices in The Brain Science Institute of Tamagawa University. Taking into account these research trends, we will investigate the dynamics and function of the associative networks of CA3 type and other related networks in relation with the top-down signals by Acetylcholine, in particular, the relationship between those top-down signals and entrainment of cortical activity during communication.
	NAME	AFFILIATION	SPECIALTY	ROLE
Leader	TSUDA, Ichiro	Hokkaido University	Mathematical Studies of Complex Systems	Organization of the research project, mathematical modeling and dynamical systems analysis
Member	FUJII, Hiroshi	Kyoto Sangyo University	Cognitive Neuroscience	Mathematical analysis and modeling
	TAKAHASHI, Yoichiro	University of Tokyo	Probability Theory and Dynamical Systems	Mathematical analysis
Collaborator	AOYAGI, Toshio	Kyoto University	Nonlinera Physics, Computational Neuroscience	Nonlinear analysis
	YAMAGUTI, Yutaka	Hokkaido University	Computational Neuroscience	Numerical analysis

[ TOP ]

Group G2

TITLE
Toward the mathematical understanding of dynamic heterogeneous patterns and its applications to life science
OBJECT
Communication can be regarded as an exchange of information via interaction and its feedback among communicators. The existence of agent called "individual"should have a tool for communication and a rich internal dynamics. Dynamics of particle patterns arsing in dissipative systems is one of the representative models. Since particle patterns are spatially localized, and therefore can be recognized as individuals. They have rich internal dynamics such as traveling, oscillation, splitting, and rotation. They can communicate either through the tails or collisions. One of our goals is to study communication dynamics among heterogeneous individuals via multiple collsions, and explore the assciated coherent dymaics. Moreover we study emergent dynamics at the system level through the communication between individuals and their environments, especially clarify the underlying global heteroclinic connections among them. Our brain is a very complex system with many meta-stable states and rich internal dynamics. When we communicate each other with various roles and cooporation or competition, it is highly possible to observe a new type of collective behaviors. therefore the essential part of such emergent dynamics, at least partially, can be understood by using the above framework.
	NAME	AFFILIATION	SPECIALTY	ROLE
Leader	NISHIURA, Yasumasa	Tohoku University	Nonlinear Analysis	Mathematical Analysis
Member	KOKUBU, Hirsohi	Kyoto University	Dynamical System Theory	Mathematical Analysis of Dynamical Systems
	UEDA, Kei-Ichi	Toyama University	Applied Analysis	Computataional Global Bifurcation Analysis
Collaborator	ARAI, Jin	Hokkaido University	Dynamical System Theory	Computational Bifurcation Analysis

[ TOP ]

Group G3

TITLE
Generation of meta-rule through dynamical systems with multiple timescales: towards a theroy of learning and evolution
OBJECT
Biological systems can autonomously generate the rule of their temporal evolution. By considering a system consisting of heterogeneous elements with different time scales, we show how some elements can play a role of controlling others. By taking advantage of the time-scale difference, chaotic itinerancy of states appears, which lead to successive generation of the rules. We will show dynamical systems with heterogeneous time-scales can adapt flexibly to external environmental changes, and establish a theoretical basis on dynamics of cognition and communication.
	NAME	AFFILIATION	SPECIALTY	ROLE
Leader	KANEKO, Kunihiko	University of Tokyo	Complex Systems	Theory and modelling by dynamical systems

[ TOP ]