Reconstructing Bifurcation Diagrams of Dynamical Systems Using Measured Time Series
Reconstructing Bifurcation Diagrams of Dynamical Systems Using Measured Time Series
复制标题
使用测量的时间序列重建动力系统的分岔图
DOI：
10.1055/s-0038-1634278
复制
发表时间：
2000
影响因子：
1.7
通讯作者：
Shunsuke Sato
中科院分区：
文献类型：
--
作者：
E. Bagarinao;K. Pakdaman;T. Nomura;Shunsuke Sato
翻译后摘要：我们提出了一种算法，从时间序列的动力系统的分岔结构重建。该方法包括在寻找一个参数化的预测函数的分叉结构类似于给定的系统。采用多项式项的非线性自回归（NAR）模型作为预测函数。在NAR模型中的适当的条款获得使用快速正交搜索方案。该方案消除了多参数优化问题，并使该方法对噪声具有鲁棒性。该算法被应用于从模拟的膜电位波形重建神经元模型的分叉图（BD）。重构的BD捕获给定系统的不同行为。此外，即使对于有限数量的时间序列，该算法也能很好地工作。
Abstract: We present an algorithm for reconstructing the bifurcation structure of a dynamical system from time series. The method consists in finding a parameterized predictor function whose bifurcation structure is similar to that of the given system. Nonlinear autoregressive (NAR) models with polynomial terms are employed as predictor functions. The appropriate terms in the NAR models are obtained using a fast orthogonal search scheme. This scheme eliminates the problem of multiparameter optimization and makes the approach robust to noise. The algorithm is applied to the reconstruction of the bifurcation diagram (BD) of a neuron model from the simulated membrane potential waveforms. The reconstructed BD captures the different behaviors of the given system. Moreover, the algorithm also works well even for a limited number of time series.
DOI：
10.2307/3620310
发表时间：
1989-10
期刊：
--
影响因子：
--
作者：
S. Wiggins
通讯作者：
S. Wiggins