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Analysis of Coupled Oscillator Networks and Application to Chemical Reaction Oscillations and Biological Rhythms

耦合振荡器网络分析及其在化学反应振荡和生物节律中的应用

基本信息

批准号：
03805028
负责人：
KAWAKAMI Hiroshi
金额：
$ 0.9万
依托单位：
The University of Tokushima
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1991
资助国家：
日本
起止时间：
1991 至 1993
项目状态：
已结题

项目摘要

Macroscopic behavior of chemical reactions, circadian rhythms of wake-sleep cycles, and oscillation patterns of neural networks is generally described by nonlinear dynamical systems. In this research we tried to analyze the mathematical models derived from these different fields of science and try to unify the qualitative behavior of these models, such as synchronization, bifurcation phenomena, multi-phase oscillations, and chaotic oscillations.1. Mathematical models of coupled oscillators derived from salt-water oscillators and BZ reactions are analyzed. We found that the different couplings cause different types of multi-phase oscillations, such as in-phase, anti-phase, or tri-phase oscillations. More detailed analysis by using the bifurcation theory is left to the future research problems.2. Two different kinds of models to human circadian rhythems are analyzed by using bifurcation theory. We found many different types od synchronizations. We analyzed also some non-synchronized states corresponding to quasi-periodic states which are compared with the results obtained by Kronauer et al. These results are also compared with the relaxation oscillator proposed by Daan et al.3. Oscillations of neural networks coupled as linear and connections are investigated from bifurcational point of view. We found some oscillation patterns are propagating along the lines and ring connection. For this new phenomenon further studies will be expected by changing the type of oscillators and connections.4. The booklet is published in which main results are collected together.

化学反应的宏观行为、觉醒-睡眠周期的昼夜节律和神经网络的振荡模式通常由非线性动力系统描述。在本研究中，我们试图分析来自这些不同科学领域的数学模型，并试图统一这些模型的定性行为，如同步，分岔现象，多相振荡和混沌振荡.分析了由盐水振子和BZ反应导出的耦合振子的数学模型。我们发现，不同的耦合导致不同类型的多相振荡，如同相，反相，或三相振荡。利用分岔理论进行更详细的分析是今后研究的问题.利用分歧理论分析了两种不同的人体昼夜节律模型。我们发现了许多不同类型的同步。我们还分析了对应于准周期态的一些非同步态，并与Kronauer等人的结果进行了比较，这些结果也与Daan等人提出的弛豫振荡器进行了比较.从分岔的观点研究了线性和连接耦合的神经网络的振动性。我们发现一些振荡模式是沿着线和环连接传播。对于这一新现象，通过改变振子的类型和连接方式，将有望得到进一步的研究.出版了一本小册子，其中收集了主要结果。