耦合Lorenz系统中的交错盆
Intermingled basins in coupled Lorenz systems
摘要：
本文考虑两个线性耦合Lorenz振子的系统，在一定的耦合强度范围内呈现混沌运动的同步。我们验证了存在的全球同步和反同步吸引子与混合盆地的吸引力，使盆地的一个吸引子是千疮百孔的洞属于盆地的其他吸引子，反之亦然。我们研究了这一现象，通过验证的数学要求的实现混合盆地，也得到了标度律，定量表征这两个盆地为这个系统的筛选。
英文摘要：
We consider a system of two identical linearly coupled Lorenz oscillators, presenting synchro- nization of chaotic motion for a specified range of the coupling strength. We verify the existence of global synchronization and antisynchronization attractors with intermingled basins of attraction, such that the basin of one attractor is riddled with holes belonging to the basin of the other attractor and vice versa. We investigated this phenomenon by verifying the fulfillment of the mathematical requirements for intermingled basins, and also obtained scaling laws that characterize quantitatively the riddling of both basins for this system.
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