Feudel Ulrike, Grebogi Celso
ICBM, Universität Oldenburg, Germany.
Phys Rev Lett. 2003 Sep 26;91(13):134102. doi: 10.1103/PhysRevLett.91.134102. Epub 2003 Sep 25.
We show that chaotic attractors are rarely found in multistable dissipative systems close to the conservative limit. As we approach this limit, the parameter intervals for the existence of chaotic attractors as well as the volume of their basins of attraction in a bounded region of the state space shrink very rapidly. An important role in the disappearance of these attractors is played by particular points in parameter space, namely, the double crises accompanied by a basin boundary metamorphosis. Scaling relations between successive double crises are presented. Furthermore, along this path of double crises, we obtain scaling laws for the disappearance of chaotic attractors and their basins of attraction.
我们表明，在接近保守极限的多稳态耗散系统中很少发现混沌吸引子。当我们接近这个极限时，混沌吸引子存在的参数区间以及它们在状态空间有界区域内吸引盆的体积会非常迅速地缩小。参数空间中的特定点，即伴随着吸引盆边界变形的双重危机，在这些吸引子的消失中起着重要作用。给出了连续双重危机之间的标度关系。此外，沿着这条双重危机的路径，我们得到了混沌吸引子及其吸引盆消失的标度律。
