Phase Synchronization in Electrically Coupled Different Neuronal Pacemakers with the Chay Model

We study the phase synchronization in different electrically coupled neuronal pacemakers with the Chay model. The numerical simulation results and the definition of the mean frequency show that phase synchronization is equal to the mean frequency locking. Nearly complete synchronization of different two coupled neuronal pacemakers is also investigated. It is shown that the cross-correlation of the membrane potential variables is suitable to judge the nearly complete synchronization.     

Suppression of Chaos and Phase Locking in Two Coupled Nonidentical Neurons under Periodic Input

Dynamical behaviour of two coupled neurons with at least one of them being chaotic is presented. Bifurcation diagrams and Lyapunov exponents are calculated to diagnose the dynamical behaviour of the coupled neurons with the increasing coupling strength. It is found that when the coupling strength increases, a chaotic neuron can be controlled by the coupling between neurons. At the same time, phase locking is studied by the maxima of the differences of instantaneous phases and average frequencies between two coupled neurons, and the inherent connection of phase locking and the suppression of chaos is formulated. It is observed that the onset of phase locking is closely related to the suppression of chaos. Finally, a way for suppression of chaos in two coupled nonidentical neurons under periodic input is suggested.     

一类非牛顿渗流方程爆破界的估计

本文利用拟线性常微分方程解的非存在性定理得到了一类拟线性反应扩散方程(非牛顿渗流方程)爆破界的估计,从而推广了半线性反应扩散方程(牛顿渗流方程)相应结果.     

一类具有二维分叉方程的积分方程的分叉

本文研究一类含参数的非线性积分方程的分叉问题,其中的积分算子的线性化算子在分叉值点处有二维零空间。利用Liapunov-Schmidt约化方法和基于系统的对称性的群论方法,得到了周期分叉解存在的充分条件。     

Dynamical Effect of Calcium Pump on Cytosolic Calcium Bursting Oscillations with IP3 Degradation

Taking account of the Ca2＋-activated degradation of inositol trisphosphate （IP3）, a one pool model of cytosolic calcium oscillation is considered to investigate the effect of the calcium pump on the Ca2＋ bursting oscillation behavior. In order to give the oscillation domain, a two-parameter bifurcation analysis of the fast subsystem is performed in the parameter plane. Different types of bursting are presented with the variation of the pump parameter, and fast-slow dynamics is used to analyze the types and generation mechanisms of the bursting oscillations. The results are instructive for understanding the role of the calcium pump played in complex intracellular calcium activities.     

Chay模型混沌节律的非稳定周期轨道

在描写神经放电的理论模型（Cahy模型）中发现有位于加周期分岔过程中的混沌节律。利用So的非稳定周期轨道检测算法研究了位于周期2和周期3之间的混沌节律的非稳定周期轨道。结果发现，靠近周期2的混沌节律中只能检测出显著的非稳定周期2轨道，而靠近周期3的混沌节律中不仅可以检测出非稳定周期2轨道，还可以检测出非稳定周期3轨道；并且该非稳定周期2轨道位置与稳定周期2位置相似，非稳定周期3位置与稳定周期3位置类似。这表明，非稳定周期轨道在神经混放电节律的动力学起着重要作用；非稳定周期轨道的结构决定着混沌节律的特征，可以用来区分混沌节律。     

一类轴对称充液陀螺系统自旋运动稳定性研究

研究了一类复杂充液旋转对称陀螺（其圆柱形容腔充有互不相溶的双元液体，且带充液圆柱中心杆）的章动振荡与其所充双元液体自由振荡之耦合问题．利用留数方法研究了系统的自旋稳态运动的稳定性条件     

Characteristics of Period-Adding Bursting Bifurcation Without Chaos in the Chay Neuron Model

A period-adding bursting sequence without bursting-chaos in the Chay neuron model is studied by bifurcation analysis. The genesis of each periodic bursting is separately evoked by the corresponding periodic spiking patterns through two period-doubling bifurcations, except for the period-1 bursting occurring via Hopf bifurcation. Hence,it is concluded that this period-adding bursting bifurcation without chaos has a compound bifurcation structure closely related to period-doubling bifurcations of periodic spiking in essence.     

多体系统动力学Lagrange方法的进展

本文综述了近年来Ｌａｇｒａｎｇｅ方法在多体系统动力学研究中的进展．介绍了３种形式的Ｌａ－ｇｒａｎｇｅ动力学方程及其数值计算方面新的研究成果     

一般力学中动力系统的非线性和混沌的最新进展与展望

本文从力学的角度出发综述了摈睛为国内外在压力系统的非线线和混沌方面的主要成果和发展前景。首先，本文阐述了非线性动力系统发展的必要性，其欠，我们详细的综述了非线性振动和局部分叉，全局分叉和混沌，非线笥随机系统的振动和分叉，和某些应用基础理论问题等四个方面近期国内外的主要研究成果。