Departamento de Físico Matemáticas, Universidad Autónoma de San Luis Potosí, Alvaro Obregón 64, Col. Centro, San Luis Potosí, Mexico.
Chaos. 2010 Mar;20(1):013116. doi: 10.1063/1.3314278.
In this paper, we present a class of three-dimensional dynamical systems having multiscrolls which we call unstable dissipative systems (UDSs). The UDSs are dissipative in one of its components but unstable in the other two. This class of systems is constructed with a switching law to display various multiscroll strange attractors. The multiscroll strange attractors result from the combination of several unstable "one-spiral" trajectories by means of switching. Each of these trajectories lies around a saddle hyperbolic stationary point. Thus, we describe how a piecewise-linear switching system yields multiscroll attractors, symmetric or asymmetric, with chaotic behavior.
在本文中，我们提出了一类具有多涡卷的三维动力系统，我们称之为不稳定耗散系统（UDS）。UDS 在其一个分量中是耗散的，但在另外两个分量中是不稳定的。该类系统采用切换律构造，以显示各种多涡卷奇异吸引子。多涡卷奇异吸引子是通过切换将几个不稳定的“一单螺旋”轨迹组合而成的。这些轨迹中的每一个都位于鞍状双曲稳定点周围。因此，我们描述了分段线性切换系统如何产生具有混沌行为的对称或不对称的多涡卷吸引子。
