放牧区碰撞振动系统的拓扑结构
Topology of Vibro-Impact Systems in the Neighborhood of Grazing
摘要：
研究了碰撞振动系统牛顿模型的擦边分岔。简要回顾了放牧族周期解存在的充分条件。讨论了这些周期解的性质。关于碰撞振动系统吸引子的拓扑结构，已有大量的结果。然而，由于所考虑的系统是强非线性的，这些吸引子可能是不可见的，或者至少对系统参数的变化非常敏感。另一方面，它们在实验和数值模拟中被观察到。我们提供（定理2）的方法，允许解释这个矛盾，并给出一个新的鲁棒的数学模型的非双曲动力系统在附近的放牧。
英文摘要：
The grazing bifurcation is considered for the Newtonian model of vibro-impact systems. A brief review on the conditions, sufficient for existence of a grazing family of periodic solutions, is given. The properties of these periodic solutions are discussed. A plenty of results on the topological structure of attractors of vibro-impact systems is known. However, since the considered system is strongly nonlinear, these attractors may be invisible or, at least, very sensitive to changes of parameters of the system. On the other hand, they are observed in experiments and numerical simulations. We offer (Theorem 2) an approach which allows to explain this contradiction and give a new robust mathematical model of the non-hyperbolic dynamics in the neighborhood of grazing.
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