Advances in Nonlinear Dynamics - Proceedings of the Second International Nonlinear Dynamics Conference (NODYCON 2021), Volume 1
Advances in Nonlinear Dynamics - Proceedings of the Second International Nonlinear Dynamics Conference (NODYCON 2021), Volume 1
复制标题
非线性动力学进展 - 第二届国际非线性动力学会议论文集 (NODYCON 2021)，第 1 卷
DOI：
10.1007/978-3-030-81162-4_31
复制
发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Blyth M
中科院分区：
文献类型：
--
作者：
Blyth M
数值延拓是一种定位和跟踪模型分岔的常用方法。基于控制的延拓（CBC）在模型不可用的情况下重新表述了这一点，允许实验者探索黑盒和物理系统的分岔结构。CBC依靠离散化来延续周期轨道。当信号包含大量高频能量时，精确的离散化变得具有挑战性，因为离散化变得越来越容易受到噪声的破坏。在这里，我们演示了如何使用局部贝叶斯模型来代替原始数据，通过自适应滤除噪声来更准确地离散信号。在霍奇金-赫胥黎和范德波尔模型的模拟中得到的合成信号上对所提出的方法进行了测试。
Numerical continuation is a popular method for locating and tracking bifurcations in a model. Control-based continuation (CBC) reformulates this for cases when a model is unavailable, allowing experimenters to explore the bifurcation structure of black-box and physical systems. CBC relies on discretisation for the continuation of periodic orbits. Accurate discretisation becomes challenging when signals contain large amounts of high-frequency energy, as the discretisation becomes increasingly vulnerable to noise corruption. Here, we demonstrate how local Bayesian models can be used in place of raw data, to more accurately discretise signals by adaptively filtering off noise. The proposed methods are tested on synthetic signals, obtained from the simulation of the Hodgkin–Huxley and van der Pol models.