The crisis induced by the property transition of a system

摘要

A simultaneous transition in the property of a system from everywhere smooth and conservative to piecewise smooth and quasi-dissipative is observed in a kicked billiard when adjusting a single controlling parameter. The transition induces a special kind of crisis, which signifies a sudden change of a typical conservative stochastic web into a transient web formed by the forward image set of the discontinuity borderline of the system function. Iterations on the transient web finally fall in an escaping hole composed of an elliptic island chain, which appears right after the threshold of the property transition. The size of the hole becomes larger as the controlling parameter increases so that the iterations escape faster. The averaged lifetime of the iterations in the transient web therefore follows a power-law with a special scaling exponent. At the same time, a fat fractal forbidden web, which appears also at the threshold,grows up and cuts off more and more parts from the original conservative stochastic web so that the remnant transient web becomes thinner and thinner. We numerically show that another power law can also describe this.