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Multiple Attractors and Itinerant Dynamics in High-dimensional Chaos

高维混沌中的多吸引子和流动动力学

基本信息

批准号：
09640455
负责人：
KANEKO Kunihiro
金额：
$ 1.79万
依托单位：
The University of Tokyo
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1998
项目状态：
已结题

项目摘要

(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 … More 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

(1)对于全局耦合映象的多吸引子状态，通过扰动后返回到自身的速率来研究吸引子的强度。结果表明，脆性（Milnor）吸引子在部分有序相具有较大的吸引盆体积.脆弱吸引子的这种优势可以通过相空间中全局吸引的鲁棒性来理解。我们将混沌巡游重新解释为Milnor吸引子网络上的动力学行为，发现噪声诱导的脆弱吸引子的选择与噪声幅值有很强的依赖关系。(2)研究了全局耦合映象的集体动力学。首先，我们用自洽的Perron-Frobenius方程阐明了Collevtie运动的机理。其次，通过引入集体李雅普诺夫指数，证明了集体混沌的存在性。第三，研究了微观外界噪声对集体运动的影响，发现集体运动的自由度随埃克斯特的增大而减小，为-logsiguma ^2 ...更多信息最终噪声方差σ ^[2]。我们展示了如何微观外部噪声可以抑制在宏观水平的自由度的数量。(3)生物组织的情况下，提出了基于数值研究的发展过程中相互作用的内部动态和繁殖的单位。多样性，离散和递归类型的形成，以及分化规则被认为是这样一个系统的自然结果。规则是通过周围单位的内部表征形成的，并且取决于内部状态和相互作用。发展过程的宏观稳健性被证明是这样一个系统的自然结果。通过引入空间局部化的机械力-化学相互作用，证明了具有生命史的多细胞生物的出现，并证明了某个噪声动力学系统具有阈值型输入依赖性，这可能与信号转导有关。然后，利用混沌和限制热浴，提出了一种在哈密顿系统中储存能量的动力系统机制。(4)我们还研究了再生单元起源的自动机模型，动力系统的不可判定性，生成符号和规则的功能动力学。少