心脏搏动模型的Hopf分岔

Hopf bifurcation to models of reactions of human heart

为了探索心脏自律活动复杂动力学行为的形成机制,本文研究外力刺激与参数扰动下心脏搏动模型的Hopf分岔问题.首先,给出系统存在Hopf分岔的一组充分条件;其次基于复规范型理论,细致刻画了Hopf分岔方向、分岔周期解及其稳定性态;最后借助数值模拟验证了理论分析结果.

In order to understand the complicated dynamics of cardiac autonomic activity , the Hopf bifurcation to models of reactions of human heart under the action of external force and parametric noise is investigated in detail and deeply . First , the conditions of the existence of Hopf bifurcation to system are obtained . Second , the direction of Hopf bifurcation , the stability of bifurcating period solutions and the expression of the bifurcating periodic solution are rigorous derived and studied by means of complex normal form theory . Finally , numerical simulations are performed to justify theoretical analysis .