Bursting Ca2+ Oscillations and Synchronization in Coupled Cells

A mathematical model proposed by Grubelnk et al. [Biophys. Chem. 94 （2001） 59] is employed to study the physiological role of mitochondria and the cytosolic proteins in generating complex Ca^2＋ oscillations, lntracellulax bursting calcium oscillations of point-point, point-cycle and two-folded limit cycle types are observed and explanations are given based on the fast/slow dynamical analysis, especially for point-cycle and two-folded limit cycle types, which have not been reported before. Furthermore, synchronization of coupled bursters of Ca^2＋ oscillations via gap junctions and the effect of bursting types on synchronization of coupled cells are studied. It is argued that bursting oscillations of point-point type may be superior to achieve synchronization than that of point cycle type.     

非线性动力学在心脏电活动研究中的应用

本文介绍了非线性动力学在心脏电活动研究中的应用。主要内容包括非线性分析指标、心率变异非线性分析、异常心率（心室振颤）的非线性分析、心脏细胞动作电位模型中的搏动节律的分叉与混沌现象及机理、混沌控制在心脏电活动研究中的应用,并对今后发展方向提出了展望。非线性动力学分析方法是研究心脏电活动的良好工具,使得解决心脏电活动中的难题成为可能。     

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

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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.     

Bifurcation and stability of spatially periodic solutions of nonlinear evolution equations with integral operators

A more general kind of nonlinear evolution equations with integral operators is discussed in order to study the spatially periodic static bifurcating solutions and their stability. At first, the necessary condition and the sufficient condition for the existence of bifurcation are studied respectively. The stability of the equilibrium solutions is analyzed by the method of semigroups of linear operators. We also obtain the principle of exchange of stability in this case. As an example of application, a concrete result for a special case with integral operators of exponential type is presented. This work was supported by the Chinese National Foundation of Natural Science