| 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)
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| 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 3-d torus forced by 1-d 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 nowhere-differentiable. 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 UC-Berkeley has found chaos and chaotic itinerancy in the olfactory bulb. We studied about the mechanism of their appearance in terms of semi-biological 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 period-doublimg, 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
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