人心脏低维动力学模型的计算机模拟

COMPUTER SIMULATION ON THE LOW-DIMENSIONAL DYNAMICAL MODEL OF HUMAN HEARTS

心脏窦房结与异位心室搏动非线性相互作用，导致调制并行收缩反常节律。本文从新的低维动力学心脏模型（双参量圆周映射）出发，研究由周期性到不规则、混沌动力学过渡的性质。模型的数值实验揭示出在双参量空间不同区域中，某些特征性步入混沌的道路和总体标度关系。一个明显特征是，在双参量空间宽广范围内观察到无穷层次的嵌套结构，即嵌在混沌带中的周期递加序列。而且，出现周期性的位置或者周期窗口的宽度，均存在普适的标度关系。另一方面，在参量空间一部分，包含相互交叠的不同周期性稳定轨道，有极复杂图象。本文结果显示，运用数值方法计算李雅普诺夫指数谱，可以基本上确定人心脏圆周映射的二维分岔结构和标度性质。

An abnormal cardiac rhythms (arrhythmia), modulated parasystole, is caused by the nonliear interaction between the sinus node and myopic Ventricular focus in the heart. A new theoretical model for low dimenSional dynandrs of the heart employing two-parameter circle maps is used to study the nature of the transition from regular periodic dynalines to ocular, chaotic dynandes. Numerical simulations of the model reveal several charaderistic routes to chaos and global scaling behavior in various sones of tWO-parameter space. One prodment feature is that chaotic and nonchaotic regions are densely interwoven over comparatiVely Wide ranges of parameter space. Universal scaling laws are found for both the length of each periodic window and their position relative to the end of period-adding sequence. On. the other hand, in one part of para￣r space, there is a extremely complex patteds of overlapping stable orbits of different periodicities displaying period-doubling and tangent bimrcations and showing a self--similar stfuctllre. This paper has shown that the two -dimensional bifurcation structure and scaling properties of able maps in human heart can be largely detendned using numerical methods based upon calculation of the Lyapunov exponent specturm.