Modeling the Sprott E Chaotic System with HAVOK Analysis Sprott E Kaotik Sisteminin HAVOK Analizi ile Modellenmesi

SOYSAL O. A., Bingöl G., GÜNAY E.

32nd IEEE Conference on Signal Processing and Communications Applications, SIU 2024, Mersin, Türkiye, 15 - 18 Mayıs 2024 identifier

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Doi Numarası: 10.1109/siu61531.2024.10600963
  • Basıldığı Şehir: Mersin
  • Basıldığı Ülke: Türkiye
  • Anahtar Kelimeler: Chaotic Systems, HAVOK Analysis, Koopman Operator, Singular Value Decomposition
  • Erciyes Üniversitesi Adresli: Evet

Özet

In this study, the Sprott E model is analyzed with the Koopman operator and the finite matrix approximation is obtained with the HAVOK (Hankel Alternative View of Koopman) method. Then, the Hankel matrix is decomposed into pieces using Singular Value Decomposition. By calculating error values for different matrix dimensions, the most appropriate matrix dimension for modeling is decided and analyses are carried out based on this value. By applying HAVOK analysis, it has been demonstrated that a dynamic structure can be represented by a linear model with a low error rate. The data obtained by modeling is compared with the time series of the original system and similar results are obtained. It is also observed that similar attractors are formed in the phase space representation of the main system and the model.