一类生物流体力学连续系统的分岔研究

Studies on the Bifurcation of a Class of Continuous Biofluiddynamical System

连续动力系统的非线性动力学研究,由于其应用的广泛性与问题的复杂性,近年来越来越受到重视。本文对一类生物流体力学中的连续系统——动脉局部狭窄时血液流动的分岔特性进行了研究,采用有限差分方法,将由偏微分方程组描述的连续动力系统约化为由常微分方程组描述的高维离散动力系统。求得了离散动力系统的平衡解并分析其稳定性,同时讨论了流场中变量空间分布的变化情况。求得了离散动力系统的前三个Lyapunov指数,以此作为系统是否发生混沌的判别条件。

On account of its wide applications and complexities, the nonlinear studies on continuous dynamical systems have been attached more weight recently. In this paper, we take the bifurcation characteristic studies on a class of continuous biofluiddynamical system: blood flow through a stenotic artery. The continuous dynamical system governed by partial differential equations is reduced into a high dimensional discrete dynamical system governed by ordinary differential equations by use of finite difference method. The equilibrium solution of the discrete dynamical system is obtained , and the solution' s stability is discussed, and the spatial distribution of variables are discussed at the same time. The first, the second and the third Lyapunov exponents of the discrete dynamical system are obtained and used as a criterion for the system whether to be chaotic.