碰撞振动系统中两种混沌门槛值的判据

Two Criteria for Chaos Threshold in Impact Vibration System

以一类简单的碰撞振动系统为例，验证了两种混沌门槛值判据的等价性。即非扰动情形具有广义同宿轨道，扰动为鞍型周期运动的碰撞振动系统中，如果相对于该鞍型周期解的相对流形上仍存在同宿轨道，则它与Ｐｏｉｎｃａｒｅ截面上稳定流形和不稳定流形横截相交是等价的。因而它可作为Ｓｍａｌｅ马蹄意义下混沌门槛值的判据，但相对流形上的判据在碰撞振动系统中显得直观简洁。

In this paper the equivalence of two criteria for chaos threshold in an impact vibration system is verified. Under undisturbed condition, there is a generalized homoclinic orbit. Under saddle periodic disturb motion condition, if there is still a homoclinic orbit in the relative manifold of saddle periodic solution, it is equivalent to the transverse intersection between stable and unstable manifold at poincare section, therefor it can be regarded as criteria for chaos threshold in the sense of horseshoe. But the criterion based on relative manifold in a impact vibration system is concise.