Parameter-dependent behaviour of periodic channels in a locus of boundary crisis
Parameter-dependent behaviour of periodic channels in a locus of boundary crisis
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边界危机处周期性通道的参数相关行为
DOI：
10.1140/epjst/e2017-70048-x
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
H. Osinga
中科院分区：
文献类型：
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作者：
J. Rankin;H. Osinga
当一个混沌吸引子超出它的吸引域并突然消失时，边界危机就发生了。如前所述，一个边界危机的轨迹是有组织的同宿或异宿切线之间的稳定和不稳定的鞍周期轨道的流形。在两个参数中，这样的切线导致曲线，但是沿着这些曲线的边界危机的轨迹沿着表现出间隙或通道，其中其他非混沌吸引子持续存在。这些吸引子是稳定的周期轨道，它们本身可以经历一系列的倍周期分岔，最终形成多分量混沌吸引子。正则双纯二维Hénon映射表现出这样的周期性通道，它们以特定的有序方式结构：每个通道的一侧由鞍结分叉限制，另一侧由倍周期级联限制到混沌;此外，所有通道似乎具有相同的方向，鞍结分叉总是在同一侧。我们研究了Ikeda映射中的边界危机轨迹，该映射模拟了激光环形腔中的能级动力学。我们发现，池田地图具有周期性的渠道，更丰富，更一般的组织比Hénon地图。利用数值延拓，我们研究了周期性通道如何依赖于第三个参数，以及它们如何分裂成具有不同性质的多个通道。
A boundary crisis occurs when a chaotic attractor outgrows its basin of attraction and suddenly disappears. As previously reported, the locus of a boundary crisis is organised by homo- or heteroclinic tangencies between the stable and unstable manifolds of saddle periodic orbits. In two parameters, such tangencies lead to curves, but the locus of boundary crisis along those curves exhibits gaps or channels, in which other non-chaotic attractors persist. These attractors are stable periodic orbits which themselves can undergo a cascade of period-doubling bifurcations culminating in multi-component chaotic attractors. The canonical diffeomorphic two-dimensional Hénon map exhibits such periodic channels, which are structured in a particular ordered way: each channel is bounded on one side by a saddle-node bifurcation and on the other by a period-doubling cascade to chaos; furthermore, all channels seem to have the same orientation, with the saddle-node bifurcation always on the same side. We investigate the locus of boundary crisis in the Ikeda map, which models the dynamics of energy levels in a laser ring cavity. We find that the Ikeda map features periodic channels with a richer and more general organisation than for the Hénon map. Using numerical continuation, we investigate how the periodic channels depend on a third parameter and characterise how they split into multiple channels with different properties.
DOI：
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发表时间：
2020
期刊：
影响因子：
--
作者：
Hironori Ito;Tetsuo Nakano;Shintaro Nomura and Kazuhiko Misawa;井上紗奈・本田秀仁・森数馬・椎名武夫・山本(前田)万里・曲山幸生・永井成美・和田有史;Guest Martin;Zin Arai
通讯作者：
Zin Arai