Saiki Yoshitaka, Yamada Michio, Chian Abraham C-L, Miranda Rodrigo A, Rempel Erico L
Graduate School of Commerce and Management, Hitotsubashi University, Tokyo 186-8601, Japan.
Research Institute for Mathematical Sciences (RIMS), Kyoto University, Kyoto 606-8502, Japan.
Chaos. 2015 Oct;25(10):103123. doi: 10.1063/1.4933267.
The unstable periodic orbits (UPOs) embedded in a chaotic attractor after an attractor merging crisis (MC) are classified into three subsets, and employed to reconstruct chaotic saddles in the Kuramoto-Sivashinsky equation. It is shown that in the post-MC regime, the two chaotic saddles evolved from the two coexisting chaotic attractors before crisis can be reconstructed from the UPOs embedded in the pre-MC chaotic attractors. The reconstruction also involves the detection of the mediating UPO responsible for the crisis, and the UPOs created after crisis that fill the gap regions of the chaotic saddles. We show that the gap UPOs originate from saddle-node, period-doubling, and pitchfork bifurcations inside the periodic windows in the post-MC chaotic region of the bifurcation diagram. The chaotic attractor in the post-MC regime is found to be the closure of gap UPOs.
在吸引子合并危机（MC）之后嵌入混沌吸引子的不稳定周期轨道（UPOs）被分为三个子集，并用于在Kuramoto-Sivashinsky方程中重构混沌鞍点。结果表明，在MC之后的 regime中，可以从危机前嵌入的预MC混沌吸引子中的UPOs重构出由危机前两个共存混沌吸引子演化而来的两个混沌鞍点。这种重构还涉及到对引发危机的中介UPO的检测，以及危机后产生的填补混沌鞍点间隙区域的UPOs。我们表明，间隙UPOs起源于分岔图的MC后混沌区域中周期窗口内的鞍结、倍周期和叉形分岔。发现MC后 regime中的混沌吸引子是间隙UPOs的闭包。
