Sataev I R, Stankevich N V
Kotelnikov Institute of Radioengineering and Electronics of RAS, Saratov Branch, Zelenaya str., 38, 410019 Saratov, Russia.
Laboratory of Topological Methods in Dynamics, National Research University Higher School of Economics, Bolshaya Pecherskaya str., 25/12, Nizhny Novgorod 603155, Russia.
Chaos. 2021 Feb;31(2):023140. doi: 10.1063/5.0038878.
We study the hyperchaos formation scenario in the modified Anishchenko-Astakhov generator. The scenario is connected with the existence of sequence of secondary torus bifurcations of resonant cycles preceding the hyperchaos emergence. This bifurcation cascade leads to the birth of the hierarchy of saddle-focus cycles with a two-dimensional unstable manifold as well as of saddle hyperchaotic sets resulting from the period-doubling cascades of unstable resonant cycles. Hyperchaos is born as a result of an inverse cascade of bifurcations of the emergence of discrete spiral Shilnikov attractors, accompanied by absorbing the cycles constituting this hierarchy.
我们研究了修正的阿尼申科 - 阿斯塔霍夫振子中的超混沌形成情况。这种情况与超混沌出现之前共振周期的二次环面分岔序列的存在有关。这种分岔级联导致了具有二维不稳定流形的鞍 - 焦点周期层次结构的诞生，以及由不稳定共振周期的倍周期级联产生的鞍型超混沌集的诞生。超混沌是由离散螺旋希利尼科夫吸引子出现的逆分岔级联产生的，同时伴随着构成该层次结构的周期的吸收。
