Gonchenko Sergey, Gonchenko Alexander, Kazakov Alexey, Samylina Evgeniya
Mathematical Center of Lobachevsky State University, 23 Prospekt Gagarina, 603950 Nizhny Novgorod, Russia.
National Research University Higher School of Economics, 25/12 Bolshaya Pecherskaya Ulitsa, 603155 Nizhny Novgorod, Russia.
Chaos. 2021 Feb;31(2):023117. doi: 10.1063/5.0037621.
We study geometrical and dynamical properties of the so-called discrete Lorenz-like attractors. We show that such robustly chaotic (pseudohyperbolic) attractors can appear as a result of universal bifurcation scenarios, for which we give a phenomenological description and demonstrate certain examples of their implementation in one-parameter families of three-dimensional Hénon-like maps. We pay special attention to such scenarios that can lead to period-2 Lorenz-like attractors. These attractors have very interesting dynamical properties and we show that their crises can lead, in turn, to the emergence of discrete Lorenz shape attractors of new types.
我们研究了所谓离散类洛伦兹吸引子的几何和动力学性质。我们表明，这种鲁棒混沌（伪双曲）吸引子可能作为通用分岔情形的结果出现，对此我们给出了现象学描述，并展示了它们在三维类亨农映射的单参数族中的某些实现示例。我们特别关注那些可能导致周期为2的类洛伦兹吸引子的情形。这些吸引子具有非常有趣的动力学性质，并且我们表明它们的危机反过来可能导致新型离散洛伦兹形状吸引子的出现。
