Assessment of chaotic features for PM₁₀ concentrations in İstanbul

Particulate matter lower or equal to 10 µm in diameter (PM₁₀) can be of natural or anthropogenic origin. Due to their impact on health and the environment, it is crucial to study the properties of PM₁₀ concentrations in a stochastic framework. In this study, the Lorenz dynamical system was applied. Daily PM₁₀ data were collected from 2011 to 2020 to carry out this study. Chaos analysis of PM₁₀ values was performed through recurrence analysis, delay time and embedding dimension, maximum Lyapunov exponent, and correlation dimension. The results showed that the PM₁₀ dynamics are characterized by nonlinearity, nonstationarity and chaos. The disorderly traits identified in the PM₁₀ time series are associated with a positive value of the maximum Lyapunov exponent and the unfolded structure of attractors when projected into phase space. Additionally, the structural patterns observed consistently during the reconstruction phase, specifically the diagonal lines divided by white bands, further indicated the presence of chaotic features. Furthermore, the delay time and embedding dimension for PM₁₀ values were computed, providing an intuitive and succinct means of assessing chaotic characteristics in the PM₁₀ time series. The results suggested that at least eight variables should be used to predict PM₁₀ concentrations.