Lin Wei, Ma Huanfei, Feng Jianfeng, Chen Guanrong
School of Mathematical Sciences, Centre for Computational Systems Biology, and Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University, Shanghai 200433, China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Oct;82(4 Pt 2):046214. doi: 10.1103/PhysRevE.82.046214. Epub 2010 Oct 19.
Finding unstable periodic orbits (UPOs) is always a challenging demand in biophysics and computational biology, which needs efficient algorithms. To meet this need, an approach to locating unstable periodic orbits in chaotic dynamical system is presented. The uniqueness of the approach lies in the introduction of adaptive rules for both feedback gain and time delay in the system without requiring any information of the targeted UPO periods a priori. This approach is theoretically validated under some mild conditions and successfully tested with some practical strategies in several typical chaotic systems with or without significant time delays.
在生物物理学和计算生物学中，寻找不稳定周期轨道（UPOs）一直是一项具有挑战性的任务，这需要高效的算法。为满足这一需求，本文提出了一种在混沌动力系统中定位不稳定周期轨道的方法。该方法的独特之处在于引入了系统反馈增益和时间延迟的自适应规则，而无需事先了解目标UPO周期的任何信息。该方法在一些温和条件下得到了理论验证，并在几个具有或不具有显著时间延迟的典型混沌系统中通过一些实际策略进行了成功测试。
