Perc Matjaz, Marhl Marko
Department of Physics, Faculty of Education, University of Maribor, Koroska cesta 160, SI-2000 Maribor, Slovenia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2004;70(1 Pt 2):016204. doi: 10.1103/PhysRevE.70.016204. Epub 2004 Jul 12.
A method for controlling unstable periodic orbits (UPOs) that have not been controllable before is presented. The method is based on detecting UPOs that are situated outside the skeleton of a chaotic attractor. The main idea is to exploit flexible parts of the attractor, which under weak external perturbations allow variable excursions of the trajectory away from its originally determined path. After the perturbation, the trajectory of the autonomous system seeks its path back to the chaotic attractor and reveals additional UPOs that are otherwise not used by the system. It is shown that these UPOs can be controlled as easily as the UPOs that form the basic chaotic attractor. The effectiveness of the proposed method is demonstrated on two different chaotic systems with very distinct response abilities to external perturbations. Additionally, some applications of the method in the fields of laser technology, information encoding, and biomedical engineering are discussed.
提出了一种控制以前无法控制的不稳定周期轨道（UPO）的方法。该方法基于检测位于混沌吸引子骨架之外的UPO。主要思想是利用吸引子的灵活部分，在弱外部扰动下，这些部分允许轨迹偏离其原本确定的路径进行可变偏移。扰动后，自治系统的轨迹会寻求回到混沌吸引子的路径，并揭示出系统原本未使用的额外UPO。结果表明，这些UPO可以像构成基本混沌吸引子的UPO一样容易地得到控制。在两个对外部扰动具有非常不同响应能力的不同混沌系统上证明了该方法的有效性。此外，还讨论了该方法在激光技术、信息编码和生物医学工程领域的一些应用。
