中文摘要：

研究两类冠状动脉系统：N型与S型．利用Melnikov方法，得到两类系统在参数条件下产生Smale马蹄意义上的混沌的阀值．通过数值模拟，不仅可以证明理论分析的正确性，同时显示出理想的分支图形和更多新的复杂动力学行为．数值模拟包括相图、势能图、同宿分支曲线和分支图，通过这些较直观地反映出系统随周期激励外力强弱变化的动态特性、复杂性和非线性特征，揭示了系统的分支形式以及通向混沌运动的道路．最后对系统的混沌运动状态进行了有效的控制．

英文摘要：

N-type and S-type, two types of coronary artery system are investigated. Applying Melnikov method,the threshold conditions for the occurrence of Smale horse chaos of the two types are obtained respectively. By numerical simulation,not only the correctness of theoretical analysis is proven but also the i- deal graphics and more new bifurcation of the complex dynamic behavior are shown. Numerical simula- tions,including phase diagram, potential diagrams, homoclinic bifurcation curve diagrams and bifurcation diagrams,are used to investigate the dynamic characteristics, the complexity and the nonlinear dynamics characteristic of the two systems, and to reveal bifurcation forms and the road leading to chaotic motion. Finally the chaotic states of motion are effectively controlled.