论文标题
创建3D地图过度振动吸引子的场景
Scenarios for the Creation of Hyperchaotic Attractors of 3D Maps
论文作者
论文摘要
我们研究了三维差异形态中过度循环吸引子出现的分叉机制，即在数值实验中具有两个阳性lyapunov指数的吸引子。为了拥有该属于吸引子的财产周期性轨道，应具有二维不稳定的不变流形。为了实现这种可能性，我们提出了几种分叉场景，其中包括与马鞍周期轨道和超临界的Neimark-Sack-Sack-Sack-Sack-Sacker分叉以及这些级联的各种组合的级联分叉分叉的级联。在论文中，这些场景由三维Mirá地图的示例说明。
We study bifurcation mechanisms for the appearance of hyperchaotic attractors in three-dimensional diffeomorphisms, i.e., such attractors whose orbits have two positive Lyapunov exponents in numerical experiments. In order to possess this property periodic orbits belonging to the attractor should have two-dimensional unstable invariant manifolds. For realization of this possibility, we propose several bifurcation scenarios that include cascades of both supercritical period-doubling bifurcations with saddle periodic orbits and supercritical Neimark-Sacker bifurcations with stable periodic orbits, as well as various combinations of these cascades. In the paper, these scenarios are illustrated by an example of the three-dimensional Mirá map.
