快-慢系统耦合的独特同步及时滞效应

项目名称： 快-慢系统耦合的独特同步及时滞效应

项目编号： No.11462013

项目类型： 地区科学基金项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 郑远广

作者单位： 南昌航空大学

项目金额： 55万元

中文摘要： 快-慢系统耦合现象普遍存在于飞行器编队飞行、工业机器人协调运作等现代工程实践中。快-慢系统的整个运动周期包含多个子运动过程，耦合后出现多种独特的同步现象，其中不同的子运动过程达到不同形式的同步。本项目研究其中独特同步现象的产生机制及时滞效应。 首先，阐述快-慢系统耦合后产生各种独特同步现象的内在机制,考察不同的耦合方式对同步特性的影响，同时对与同步特性相关的参数区域进行划分，揭示新的同步现象和同步特性。其次，在不同的耦合方式下，分别阐述快变量和慢变量中的时滞对快-慢系统耦合同步特性的影响机制，揭示时滞导致的各种新的同步现象和同步特性，并进一步结合以时滞为参数的动力学分岔图，揭示时滞导致的各种同步转迁现象及其内在机制。最后，研究快-慢系统中分岔延时、慢通过效应等特有的动力学行为之间的同步现象，阐述其同步特性及时滞效应。 本项目的研究为现代工程实践提供理论指导，也丰富了非线性科学的基础理论。

中文关键词： 非线性动力学；运动稳定性

英文摘要： The phenomenon of coupled slow-fast systems is common in modern engineering，such as formation flying of aerocraft, cooperation of industrial robot and so on. The whole evolutionary period of slow-fast system includes several sub evolutionary processes, and the coupled slow-fast systems can exihibit particular synchronization with different synchronization mode of each sub evolutionary process. This research project focuses on the underlying mechanism of the generation of the particular synchronization and time-delay effects. Firstly, study the underlying mechanism of the generation of particular synchronization phenomenon in coupled slow-fast systems, and consider the effects of coupling mode on the characteristics of synchronization, and divide the parameter regions, which is relevant to the characteristics of synchronization, and uncover novel synchronization phenomena and characteristics. Secondly, state the effects of time-delay, which is within the fast variables or the slow variables, on the characteristics of synchronization in coupled slow-fast systems with different couping mode, and uncover some novel synchronization phenomena and characteristics resulted from time-delay, and moreover, depending on the dynamical bifurcation diagram with bifurcation parameter time-delay, uncover the underlying mechanism of the generation of synchronization transitions resulted from time-delay. In the last, investigate the synchronization phenomenon between the special dynamics in slow-fast systems,such as the delayed bifurcation, slow passage effect and so on, and state the characteristics of synchronization and time-delay effects. This research project can provide modern engineering with theoretical guidance, and enrich the results of nonlinear science.

英文关键词： Nonlinear dynamics;Stability