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Stabilizing unstable periodic orbits in higher dimensional systems based on stability transformation method

机译:基于稳定性变换法的高维不稳定周期轨道的稳定

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In this study, we consider stabilizing unstable periodic orbits of a continuous-time chaotic system based on stability transformation method. In previous work, we proposed a procedure which transforms stability of some fixed points embedded in chaotic attractor without information of its location. The procedure is powerful control method to stabilize unknown unstable periodic orbits, however it has considered only simple case such that an 1-dimensional (1-D) map can be used as embedded return map. In this paper, we try to extend our method to higher dimensional and continuous-time systems. As an example, we show a process to stabilize fixed points in 2-D chaotic map and unstable periodic orbits of 4-D chaos generator. By applying the proposed method to unstable fixed points of Lozi map and unstable periodic orbits of a hysteresis chaos generator, we confirm the effectiveness of the method.
机译:在这项研究中,我们考虑基于稳定性变换方法来稳定连续时间混沌系统的不稳定周期轨道。在先前的工作中,我们提出了一种程序,该程序可以变换嵌入在混沌吸引子中的某些固定点的稳定性,而无需知道其位置信息。该过程是稳定未知不稳定周期轨道的强大控制方法,但是它仅考虑了简单情况,即一维(1-D)映射可用作嵌入式返回映射。在本文中,我们尝试将我们的方法扩展到高维和连续时间系统。例如,我们展示了稳定二维混沌图谱中的固定点和4-D混沌生成器的不稳定周期轨道的过程。通过将该方法应用于Lozi映射图的不稳定定点和磁滞混沌发生器的不稳定周期轨道,我们证实了该方法的有效性。

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