第二届国际动力学、振动与控制学术会议(ICDVC-2006)介绍

动力学、振动与控制是力学理论和应用的重要分支,也是现代科学技术十分活跃的前沿研究领域.从经典定义的角度来看,动力学与控制学科主要研究牛顿力学的一般原理和一切宏观离散系统的动力学现象.由于连续介质力学问题可以经过离散化而变成有限自由度系统的问题来处理,并且现代动力学理论可以推广到连续系统,因而动力学与控制理论中的原理和方法也同样适用于连续介质力学.     

odgkin—Huxley方程的Hopf分岔的研究

数值计算发现Ｈｏｄｇｋｉｎ－ｈｕｘｌｅｙ（ＨＨ）方程中存在亚临界Ｈｏｐｆ分岔。对ＨＨ方程进行具体分析，得到简化ＨＨ方程用规范型（ｎｏｒｍａｌ ｆｏｒｍ）理论对简化ＨＨ进行定一性分析，发现简化ＨＨ方程反映了ＨＨ方程的分岔性态。     

神经元动力系统的随机共振现象

本文首先简单介绍了随机共振和随机自共振的概念、物理意义、理论模型和实验验证。在此基础上。着重对高度非线性的神经系统电活动的随机共振现象进行了介绍。内容包括神经元动力系统的非线性、神经元随机共振、随机自共振的实验和理论解释。     

树形多体系统动力学的隐式数值算法

研究了树形多体系统动力学的隐式算法．用矩阵形式给出了多体系统的正则方程及其右端函数的Ｊａｃｏｂｉ矩阵，并给出该矩阵的分块算法和对角隐式Ｒｕｎｇｅ－Ｋｕｔａ法（ＤＩＲＫＭ）以及隐式辛Ｒｕｎｇｅ－Ｋｕｔａ法（ＩＳＲＫＭ）．该算法便于编程计算，能提高计算效率，保持长期计算的稳定性．并用算例说明该算法的有效性     

Comparison of Synchronization Ability of Four Types of Regular Coupled Networks

We investigate the synchronization ability of four types of regular coupled networks. By introducing the proper error variables and Lyapunov functions, we turn the stability of synchronization manifold into that of null solution of error equations, further, into the negative definiteness of some symmetric matrices, thus we get the sufficient synchronization stability conditions. To test the valid of the results, we take the Chua's circuit as an example. Although the theoretical synchronization thresholds appear to be very conservative, they provide new insights about the influence of topology and scale of networks on synchronization, and that the theoretical results and our numerical simulations are consistent.     

Phase synchronization and its bursting neurons： theoretical transition in two coupled and numerical analysis

It is crucially important to study different synchronous regimes in coupled neurons because different regimes may correspond to different cognitive and pathological states. In this paper, phase synchronization and its transitions are discussed by means of theoretical and numerical analyses. In two coupled modified Morris-Lecar neurons with a gap junction, we show that the occurrence of phase synchronization can be investigated from the dynamics of phase equation, and the analytical synchronization condition is derived. By defining the phase of spike and burst, the transitions from burst synchronization to spike synchronization and then toward nearly complete synchronization can be identified by bifurcation diagrams, the mean frequency difference and time series of neurons. The simulation results suggest that the synchronization of bursting activity is a multi-time-scale phenomenon and the phase synchronization deduced by the phase equation is actually spike synchronization.     

旋涡诱发振动中的次谐,超谐和主共振问题

本文利用尾流－结构振子模型去研究弹性结构的旋涡诱发振弱和强的相互作用下的共振动力学特性。我们借助于多重尺度法和范式方法，得到次谐、超谐和主共振周期运动和呼种定量和定性结果。     

一类非线性耦合振子的模态分析

本文研究了一非线性耦合振子系统的相似和非相似模态，用模态的方法分析和讨论此系统单振子振动和两振子的同步或反步周期运动，并且给出数值结果，以考察非线性模态的有效性。     

Codimension-Two Bifurcation Analysis in Hindmarsh-Rose Model with Two Parameters

Bifurcation phenomena in a Hindmarsh Rose neuron model are investigated. Special attention is paid to the bifurcation structures of two parameters, where codimension-two generalized-Hopf bifurcation and fold-Hopf bifurcation occur. The classification of firing patterns as well as the transition mechanism in different regions on the parameter plane are obtained.