Investigation of Wavelet Entropy of Spinor Type Instanton Solutions in a 4-Dimensional Model

Abstract

In recent years, many methods have been proposed in various fields to investigate the properties of orbits of nonlinear dynamical systems. In this study, the characteristics of the orbits of spinor-type instanton solutions in the four-dimensional Gursey model via Heisenberg ansatz is investigated. The orbits of spinor-type instanton solutions are analyzed by Shannon wavelet entropy (WE) method. In order to analyze the regular or irregular states of the orbits of spinor-type instanton solutions, WE spectrum and WE in phase space are studied. It is observed that spinor-type instanton solutions have regular orbits around the fixed point and irregular orbits for other points. According to this study, WE can be used to observe the entropy evolution of nonlinear dynamical systems in phase space.

Keywords

• Nonlinear dynamical systems
• spinor-type instanton
• wavelet entropy
• phase space.

4 Boyutlu Modelde Spinör Tipi İnstanton Çözümlerinin Dalgacık Entropisinin İncelenmesi

Öz

Son yıllarda, doğrusal olmayan dinamik sistemlerin yörüngelerinin özelliklerini araştırmak için çeşitli alanlarda birçok yöntem önerilmiştir. Bu çalışmada, Heisenberg anzatı aracılığıyla bulunan dört boyutlu Gürsey modeldeki spinör tipi instanton çözümlerinin yörüngelerinin karakteristiği incelenmiştir. Spinör tipi instanton çözümlerinin yörüngeleri, Shannon dalgacık entropisi – wavelet entropy (WE) yöntemiyle analiz edilmektedir. Spinör tipi instanton çözümlerinin yörüngelerinin düzenli veya düzensiz durumlarını analiz etmek için faz uzayında WE ve WE spektrumu üzerine çalışılmaktadır. Spinör tipi instanton çözümlerinin kararlı nokta etrafında düzenli yörüngelere ve diğer noktalar için düzensiz yörüngelere sahip olduğu gözlemlenmiştir. Bu çalışmaya göre, faz uzayında WE doğrusal olmayan dinamik sistemlerin entropi evrimini gözlemlemek için kullanılabilir.

Anahtar Kelimeler

• Doğrusal olmayan dinamik sistemler
• spinör tipi instanton
• dalgacık entropisi
• faz uzayı

Kaynakça

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