A theoretical study for the mechanism of information processing of chaos in central nervous systems

中枢神经系统混沌信息处理机制的理论研究

• 批准号: 05836028
• 负责人: TSUDA Ichiro
• 金额: $ 1.28万
• 依托单位: Hokkaido University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1993
• 资助国家: 日本
• 起止时间: 1993 至 1994
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-05836028/
• 关键词: Nowhere-differentiable 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

(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 … More 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

(1)“奇异非混沌”是一类新的混沌动力系统。在本研究中，我们成功地构建了它的数学模型，可以是一个刻板的分析，我们澄清了机制的出现奇怪的非混沌。我们的模型是一个三维环面被迫一维混沌。构造了一个公理系统，使得该公理系统是阿克西姆A。这个公理A系统具有一般意义上的不变流形不可微的性质。本文的研究再次证明了在一类结构稳定的动力系统中，同时存在具有光滑不变流形和不具有光滑流形的两种不同的动力系统，其中不具有光滑流形的动力系统仅具有Hoelder连续性.同时阐明了这类吸引子的Hausdorff维数和拓扑维数相差不止一个的机理。(2)研究了混沌巡游在神经网络中的一种可能作用。我们的结论是，网络的非线性可分性的能力， ...更多信息 模式和额外的学习可以在网络创建混乱巡回时发展。(3)加州大学伯克利分校的沃尔特·弗里曼（Walter Freeman）发现了嗅球中的混沌和混沌巡回。我们从半生物神经网络的角度研究了它们出现的机理。该网络是由阻尼振荡器作为一个单元。只有在单元之间存在兴奋性突触连接的情况下，网络才会显示出混乱。当引入赫布学习时，观察到混沌巡游和行波，这两者都在实验中观察到。此外，我们研究了一种新类型的强迫振荡，它源于一个网络同步的呼吸周期。强迫的函数形式具有指数增加和指数减少的部分，而在通常的强迫系统研究中，周期强迫是由正弦函数给出的。我们观察到典型的分岔，如倍周期，不稳定性，危机作为连续变化的功能形式的强迫项。(4)我们从动力系统的观点来研究大脑的宏观活动。通过对耦合映象格子中李雅普诺夫指数的估计和观测到的统计反常性，我们得出结论：大小为10^<**>3 ~ 10^<**>10的神经网络必须被视为非线性系统，而不是线性系统，甚至不能被视为宏观系统。少

项目成果

K.Kaneko and I.Tsuda: "Constructive complexity and artificial reality : an introduction." Physica D. 75. 1-10 (1994)

K.Kaneko 和 I.Tsuda：“构造性复杂性和人工现实：简介”。

K.Kaneko and I.Tsuda: "Constructive complexity and antificial reality:an introduction" Physica D. 75. 1-10 (1994)

K.Kaneko 和 I.Tsuda：“构造复杂性和反现实现实：简介”Physica D. 75. 1-10 (1994)

I.Tsuda: "Dynamic binding theory is not plausible without chaotic oscillations" Behavioral and Brain Sciences. 6. 475-476 (1993)

I.Tsuda：“如果没有混沌振荡，动态结合理论是不合理的”行为与脑科学。

O.E.Rossler,J.L.Hudson,C.Knudsen and I.Tsuda: "Nowheu-differintiable attractors" Int.J.of Intelligent. 10. 5-23 (1995)

O.E.Rossler、J.L.Hudson、C.Knudsen 和 I.Tsuda：“Nowheu 可微吸引子”Int.J.of Intelligence。

I.Tsuda: "How can chaos be a cognitive processor?" Proc.of the 7th Toyota Int.Workshop on“Toward the harnessing of chaos". (印刷中). (1994)

I.Tsuda：“混沌如何成为认知处理器？”第七届丰田国际研讨会的“利用混沌”（1994 年）。