|Budget Amount *help
¥2,800,000 (Direct Cost : ¥2,800,000)
Fiscal Year 1998 : ¥1,200,000 (Direct Cost : ¥1,200,000)
Fiscal Year 1997 : ¥1,600,000 (Direct Cost : ¥1,600,000)
(1) Strength of attractor is studied by the return rate to itself after perturbations, for a multi-attractor state of a globally coupled map. It is found that fragile (Milnor) attractors have a large basin volume at the partially ordered phase. Such dominance of fragile attractors is understood by robustness of global attraction in the phase space. We reinterpret chaotic itinerancy as the dynamics over Milnor attractor network, Noise-induced selection of fragile attractors is found that has a sharp dependence on the noise amplitude.
(2) Collective dynamics of globally coupled maps is studied. First, we have clarified the mechanism of collevtie motion in terms of self-consistent Perron-Frobenius equation. Second, existence of collective chaos is shown by introducing the collective Lyapunov exponent. Third, effect of microscopic external noise on the collective motion is studied, to find that the number of degrees of freedom in the collective motion decreases as-logsiguma^2 with the exter
nal noise variance siguma^2. We show how the microscopic external noise can suppress the number of degrees of freedom in macroscopic level.
(3) A scenario for biological organization is proposed, based on numerical studies of the developmental process of interacting units with internal dynamics and reproduction. Diversification, formation of discrete and recursive types, and rules for differentiation are found as a natural consequence of such a system. The rule is formed through the internal representation of the surrounding units, and depends both on internal state and on interaction. The macroscopic robustness of the developmental process is shown to be a natural consequence of such a system. By introducing spatially localized mechano-chemical interactions, the emergence of a multi-cellular organism with a life history is demonstrated.
We have also shown that a certain noisy dynamical system shows threshold-type inpute dependence, in possible connection with signal transduction. Fur thermore, a dynamical systems mechanism to store energy in a Hamiltonian system is proposed with the use of chaos and restricted heat-bath.
(4) We have also studied tile automaton model for the origin of reproduction unit, undecidability in terms of dynamical systems, functional dynamics to generate symbols and rules. Less