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Ma, Fei,Ding, Zongze,Cheng, Xianian Korean Society of Applied Entomology 2001 Journal of Asia-Pacific Entomology Vol.4 No.1
The brown planthopper (BPH: Nilaparvata lugens(St${\aa}$l) occurrence time series data from June to November of 1986-1998 in Taihu Lake area, Jingsu province, China, were used to calculate correlation dimension ($D_2$(m)) and the second-order Renyientropy($k_2$). Based on the methods of the approximation Kolmogorov's entropy and phase space extension, the average predictable time scale of BPH occurrence system was computed. The results indicate that the BPH occurrence system is a chaotic system with fractal dimension ($D_2$(m)) form 4.34 to 4.43 and saturation embedding dimension $m_c =10$. And it could be inferred that the BPH occurrence evolution would be described by 5-10 steps required by the development of these chaotic attractors in the multi-dimensional phase space. The average predictable time scale is about 114.0-253.2 days, and the really predictable time scale of 79.0-175.5 days resulted from the e-folding expansion of trajectories in phase space. The effect of the lag time $\tau$ was examined during the continuation of phase space. And it was found that ($D_2$(m)) is convergent with respect to $\tau$. While the BPH occurrence time series data every four days were analyzed by the continuation of phase space with $\tau$=5, the coordinate components was independent of each other, and the dynamically characteristic quantity of the system was stable and reliable.
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