Nonlinear normal modes and their superposition in a two degrees of freedom asymmetric system with cubic nonlinearities

This paper investigates nonlinear normal modes and their superposition in a two degrees of freedom asymmetric system with cubic nonlinearities for all nonsingular conditions, based on the invariant subspace in nonlinear normal modes for the nonlinear equations of motion. The focus of attention is to consider relation between the validity of superposition and the static bifurcation of modal dynamics. The numerical results show that the validity has something to do not only with its local restriction, but also with the static bifurcation of modal dynamics. Project Supported by the National Natural Science Foundation and PSF of China     

The motion of organization center of scroll waves in excitable media with single diffusion

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎ１９７３,Ｗｉｎｆｒｅｆｉｒｓｔｄｉｓｃｏｖｅｒｅｄｔｈｅｔｈｒｅ＿ｄｉｍｅｎｓｉｏｎａｌｓｃｒｏｌｗａｖｅｉｎｔｈｅＢｅｌｏｕｓｏｖ＿Ｚｈａｂｏｔｉｎｓｋｙｒｅａｇｅｎｔ．Ｉｎ１９８３,Ｗｅｌｓｈｓｈｏｗｅｄｔｈｅｅｘｉ...     

van der Pol-Duffing时滞系统的稳定性和Hopf分岔

研究了具有三次项的ｖａｎ ｄｅｒ Ｐｏｌ－Ｄｕｆｆｉｎｇ非线性时滞系统的稳定性和Ｈｏｐｆ分岔,分析了当线性化特征方程随两参数（时滞量和增益系数）变化时特征根的分布;证明了Ｈｏｐｆ分岔的存在性,通过构造中心流形并且使用范式方法给出的Ｈｏｐｆ分岔的方向以及周期解的稳定性,讨论时滞量对该系统的Ｈｏｐｆ分岔的影响。     

在激发介质中单扩散回卷波组织中心的运动

应用奇异摄动方法,讨论了在单扩散型激发介质中无扭曲的三维回卷波组织中心的运动规律.确定了无扭曲的组织中心的曲率关系和线性律,这些结果具有明显的物理意义,而且与实验符合得很好.     

Fourier spectral approximation to long-time behavior of three dimensional Ginzburg-Landau type equation*

In this paper, we consider a three dimensional Ginzburg–Landau type equation with a periodic initial value condition. A fully discrete Galerkin–Fourier spectral approximation scheme is constructed, and then the dynamical properties of the discrete system are analyzed. First, the existence and convergence of global attractors of the discrete system are proved by a priori estimates and error estimates of the discrete solution, and the numerical stability and convergence of the discrete scheme are proved. Furthermore, the long-time convergence and stability of the discrete scheme are proved. *This work was supported by the National Natural Science Foundation of China (No.: 10432010 and 10571010)     

Border collision bifurcations in 3D piecewise smooth chaotic circuit

A variety of border collision bifurcations in a three-dimensional (3D) piecewise smooth chaotic electrical circuit are investigated. The existence and stability of the equilibrium points are analyzed. It is found that there are two kinds of non-smooth fold bifurcations. The existence of periodic orbits is also proved to show the occurrence of non-smooth Hopf bifurcations. As a composite of non-smooth fold and Hopf bifurcations, the multiple crossing bifurcation is studied by the generalized Jacobian matrix. Some interesting phenomena which cannot occur in smooth bifurcations are also considered.     

具有刚性约束的非线性动力系统的局部映射方法

对具有刚性约束的n维非线性动力系统进行研究,建立了该类系统在刚性约束附近的局部映射关系.又根据连续性和横截性条件,通过几何方法推导并证明了局部映射的Jacobi矩阵的解析式.然后,通过引入局部映射,并利用Poincar啨映射方法,基于Floquet理论对刚性约束的n维非线性动力系统的周期运动的稳定性和分岔进行分析,给出了该类系统Poincar啨映射的Jacobi矩阵的计算方法.最后,以一类刚性约束的非线性动力系统为例,揭示了局部映射在其动力学分析中的重要作用.     

Correlated noise induced spatiotemporal coherence resonance in a square lattice network

The effects of additive correlated noise, which is composed of common Gaussian white noise and local Gaussian colored noise, on a square lattice network locally modelled by the Rulkov map are studied. We focus on the ability of noise to induce pattern formation in a resonant manner. It is shown that local Gaussian colored noise is able to induce pattern formation, which is more coherent at some noise intensity or correlation time, so it is able to induce spatiotemporal coherence resonance in the network. When common Gaussian white noise is applied in addition, it is seen that the correlated noise can induce coherent spatial structures at some intermediate noise correlation, while this is not the case for smaller and larger noise intensities. The mechanism of the observed spatiotemporal coherence resonance is discussed. It is also found that the correlation time of local colored noise has no evident effect on the optimal value of the noise strength for spatiotemporal coherence resonance in the network.     

第二届认知神经动力学国际会议简介

<正>对于大脑的智能之谜,我们还是可望而不可及.大脑的智能牵涉到从量子到社会的各个层次,为了研究这个问题,必须要用到各种学科知识,从各种角度来进行研究.其中一个非常重要的途径就是把大脑作为一个动力学系统来进行研究.许多科学家认识到为了研究脑,需要     

Dynamics of firing patterns, synchronization and resonances in neuronal electrical activities： experiments and analysis

Recent advances in the experimental and theoretical study of dynamics of neuronal electrical firing activities are reviewed. Firstly, some experimental phenomena of neuronal irregular firing patterns, especially chaotic and stochastic firing patterns, are presented, and practical nonlinear time analysis methods are introduced to distinguish deterministic and stochastic mechanism in time series. Secondly, the dynamics of electrical firing activities in a single neuron is concerned, namely, fast-slow dynamics analysis for classification and mechanism of various bursting patterns, one- or two-parameter bifurcation analysis for transitions of firing patterns, and stochastic dynamics of firing activities （stochastic and coherence resonances, integer multiple and other firing patterns induced by noise, etc.）. Thirdly, different types of synchronization of coupled neurons with electrical and chemical synapses are discussed. As noise and time delay are inevitable in nervous systems, it is found that noise and time delay may induce or enhance synchronization and change firing patterns of coupled neurons. Noise-induced resonance and spatiotemporal patterns in coupled neuronal networks are also demonstrated. Finally, some prospects are presented for future research. In consequence, the idea and methods of nonlinear dynamics are of great significance in exploration of dynamic processes and physiological functions of nervous systems.