A theoretical study for the mechanism of information processing of chaos in central nervous systems
Project/Area Number  05836028 
Research Category 
GrantinAid for General Scientific Research (C)

Allocation Type  Singleyear Grants 
Research Field 
非線形科学

Research Institution  Hokkaido University 
Principal Investigator 
TSUDA Ichiro Faculty of Science, Hokkaido University Professor, 理学部, 教授 (10207384)

Project Period (FY) 
1993 – 1994

Project Status 
Completed(Fiscal Year 1994)

Budget Amount *help 
¥2,000,000 (Direct Cost : ¥2,000,000)
Fiscal Year 1994 : ¥1,000,000 (Direct Cost : ¥1,000,000)
Fiscal Year 1993 : ¥1,000,000 (Direct Cost : ¥1,000,000)

Keywords  Nowheredifferentiable attractors / chaotic itinerancy / pattern recognition / Newral Networks / Forced oscillation / Bifurcations / Chaotic neural networks / カオス / 非線形神経回路 / リアプノフ指数 / 相互情報量 / 非対称シグモイド関数 / 集合電位 / 記憶の保持 / 学習 
Research Abstract 
(1) It is known that 'strange nonchaos' is a new class of chaotic dynamical systems. In the present study, we succeeded in constructing its mathematical model that could be a stereotype for analyzes, and we clarified the mechanism for the appearance of strange nonchaos. Our model is a 3d torus forced by 1d chaos. It was constructed such that the system is Axim A.This Axiom A systems has the property in a generic sense that invariant manifold is nowheredifferentiable. This study strengthens again the statement that there coexist two distinct dynamical systems with smooth invariant manifold and without smoothness in a class of structural stable dynamical systems, the latter of which has only Hoelder continuity. Also the mechanism was clarified that the Hausdorff and the topological dimensions of this type of attractors differs by more than one. (2) We studied a possible role of chaotic itinerancy in neural networks. We concluded that the network abilities for nonlinear separability of
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patterns and additional learning can develop when the network creates chaotic itinerancy. (3) Walter Freeman in UCBerkeley has found chaos and chaotic itinerancy in the olfactory bulb. We studied about the mechanism of their appearance in terms of semibiological neural networks. The network is constituted of damped oscillators as a unit. The nets showed chaos only in the case with excitatory synaptic connections between units. When a Hebbian learning is introduced, chaotic itinerancy and traveling waves were observed, both of which have been observed in the experiment. Furthermore, we investigated a new type of forced oscillations which stems from a network synchronization with a period of respiration. The functional form of forcing has an exponential increasing and decreasing parts, while in usual forced systems' study a periodic forcing is given by a sinusoidal function. We observed typical bifurcations such as perioddoublimg, intermittency, and crisis as continuously varing the functional form of forcing term. (4) We studied a macroscopic activities of brain from the dynamical systems viewpoint. We concluded from the estimation of the Lyapunov exponents and an observed statistical anormality in coupled map lattices that neural networks of the size of 10^<**>3 to 10^<**>10 must be viewed as a nonlinear systems, not linear ones as even a macroscopic system. Less

Report
(3results)
Research Output
(24results)