论文标题
使用图像处理和非线性时间序列分析对时空模式的分形维度分析
Fractal dimension analysis of spatio-temporal patterns using image processing and nonlinear time-series analysis
论文作者
论文摘要
本文介绍了通过数值求解Swift Hohenberg（SH）方程生成的时空模式的分形维度的估计。通过评估最大的Lyapunov指数，将模式转换为空间序列（类似于时间序列），该系列被证明是混乱的。我们已经在这些空间数据上应用了几种非线性时间序列分析技术，例如破坏性波动和重新缩放范围，以获取HURST指数值，这些值揭示了空间串联数据与远距离相关。我们估计了赫斯特和幂律指数的分形维，发现该值位于1到2之间。我们方法的新颖性在于使用图像使用图像转换为数据转换和空间串联分析技术，对于实验获得的图像至关重要。
This article deals with the estimation of fractal dimension of spatio-temporal patterns that are generated by numerically solving the Swift Hohenberg (SH) equation. The patterns were converted into a spatial series (analogous to time series) which were shown to be chaotic by evaluating the largest Lyapunov exponent. We have applied several nonlinear time-series analysis techniques like Detrended fluctuation and Rescaled range on these spatial data to obtain Hurst exponent values that reveal spatial series data to be long range correlated. We have estimated fractal dimension from the Hurst and power law exponent and found the value lying between 1 and 2. The novelty of our approach lies in estimating fractal dimension using image to data conversion and spatial series analysis techniques, crucial for experimentally obtained images.
