Nonlinear dynamics approach to cooperative phenomena in active element systems and its application to the study of biological rhythms

活性元件系统中协同现象的非线性动力学方法及其在生物节律研究中的应用

• 批准号: 61540274
• 负责人: SHIINO Masatoshi
• 金额: $ 0.83万
• 依托单位: Tokyo Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1986
• 资助国家: 日本
• 起止时间: 1986 至 1987
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-61540274/
• 关键词: Nonequilibrium phase transition; H-theorem; Fluctuation-dissipation theorem Nonlinear Fokker-Planck equation; Entropy production; マッキーンプロセス; リヤプノフファンクショナル; 同期; ひきこみ; 非平衡熱力学; クリティカル・スローイングダウン; リセプノフ・ファンクショナル

The present project aims at studying the possibility of developing the concepts of phase transitions exhibited by nonequilibrium and (or) nonthermodynamic systems from the statistical mechanics point of view.Our research has a potential applicability to investigations of cooperative phenomena observed in systems consisting of active elements such as living cells in biological organizations. In order to make a systematic and rigorous analysis we have employed stochastic models of infinitely many particle systems with mean-field interaction. The systems consist of infinitely many coupled nonlinear oscilltors subjected to the influence of external noise and are described by sets of infinitely many coupled langevin equations. Noting that the stochastic systems reduce to nonlinear Fokker-Planck equations (NFPE) capable of exhibiting bifurcations associated with phase transitions of the systems,we have made full use of the NFPE to get insights into dynamical properties of the systems associa … More ted with the bifurcations.The NFPE are classified into two categories. The first type is characterized by the potential condition and has a close resemblance to the case of thermodynamic systems. In this case attractors of the NFPE corresponding to the ergodic components are of fixed point type. The second type refers to the case without potential condition in which attractors are allowed to be of limit-cycle or chaos type. For the first type case,we have elucidated asymptotic approach to equilibrium of the system by proving an H-theorem on the NFPE and conducted nonlinear stability analysis with the H-functional being taken as a Lyapunov functional. Dynamical behavior of fluctuations has also been investigated,by employing Fluctuation-Dissipation theorem,to show the appearance of critical slowing down in the vicinity of the bifurcation points as well as to obtain power spectra and correlation functions of the fluctuations. With regard to the second case we obtained a new type of phase transition,in which as external noise power is decreased the system undergoes Hopf-bifurcation and the probability distribution given by the solution to the NFPE begins to rotate with a certain frequency. Less

本课题的目的是从统计力学的观点出发，研究发展非平衡和（或）非热力学系统的相变概念的可能性，对生物组织中的活细胞等活性元素组成的系统中观察到的协同现象的研究具有潜在的应用价值。为了进行系统和严格的分析，我们采用了随机模型的无穷多个粒子系统的平均场相互作用。该系统由无穷多个耦合非线性阻尼器组成，受外部噪声的影响，并由无穷多个耦合朗之万方程组描述。注意到随机系统可归结为非线性Fokker-Planck方程（NFPE），该方程能够表现出与系统相变相关的分岔，我们充分利用NFPE来深入了解系统的动力学性质，并将其应用于随机系统的动力学研究中。 ...更多信息 NFPE分为两类。第一种类型以势条件为特征，与热力学系统的情况非常相似。在这种情况下，NFPE的吸引子对应的遍历组件是固定点类型。第二类是指没有势条件的情形，其中允许吸引子是极限环或混沌型。对于第一种情况，我们已经阐明了渐近方法的平衡系统的NFPE上证明的H-定理，并进行非线性稳定性分析与H-功能作为一个李雅普诺夫功能。利用涨落耗散定理研究了涨落的动力学行为，给出了涨落在分岔点附近的临界慢化现象以及涨落的功率谱和关联函数。关于第二种情况，我们得到了一种新的类型的相变，在这种情况下，随着外部噪声功率的减少，系统经历Hopf分岔，并且由NFPE的解给出的概率分布开始以一定的频率旋转。少

项目成果

椎野正寿: Physical Review A.

椎野正俊：《物理评论 A》

椎野正寿: Physics Letter.

椎野正俊：《物理快报》。