基于图像处理和非线性时间序列分析的时空模式分维分析
Fractal dimension analysis of spatio-temporal patterns using image processing and nonlinear time-series analysis
摘要：
本文讨论了由数值求解Swift Hohenberg（SH）方程产生的时空模式的分形维数的估计。模式被转换成一个空间序列（类似于时间序列），这是通过评估最大的李雅普诺夫指数是混乱的。我们已经应用了几个非线性时间序列分析技术，如去趋势波动和重新标度范围对这些空间数据，以获得赫斯特指数值，揭示空间序列数据是长期相关的。我们估计分形维数的赫斯特指数和幂律指数，发现值介于1和2之间。我们的方法的新颖性在于估计分形维数使用图像到数据的转换和空间序列分析技术，实验获得的图像至关重要。
英文摘要：
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.
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