4-Boyutlu Hiperkaotik Pang Sisteminin Kesir Dereceli Analizi ve Adaptif Senkronizasyonu

Abstract

Kesir dereceli hesaplamalar doğrusal olmayan sistemlerin dinamiklerini analiz etmekte kullanılan ve daha kesin sonuçlar elde edilmesini sağlayan etkili bir yöntemdir. Bu çalışmada, öncelikle 4 boyutlu Pang sistemi tanıtılmış ve hiperkaotik yapısını gösteren dinamik analizleri verilmiştir. Daha sonra sistemin kesir dereceli hesaplamaları yapılarak farklı kesir dereceleri için sahip olduğu dinamikler incelenmiştir. Bu kapsamda, Lyapunov üstelleri ve faz-uzayı gösteriminden elde edilen sonuçlara göre, Pang sistemi farklı kesir derecelerinde periyodik, kaotik ve hiperkaotik davranışlar sergilemektedir. Çalışmanın sonunda elde edilen sonuçlar, sistemin 3,52 kesir derecesi için hiperkaotik yapıda olduğunu göstermiştir. Elde edilen bu sonuç, tamsayı dereceli modele göre kesir dereceli yapı ile daha kesin sonuçlara ulaşıldığını doğrulamıştır. Çalışmanın ilerleyen kısmında, elde edilen kesir dereceli sistemin adaptif senkronizasyonu gerçekleştirilmiştir. Üç farklı durum incelenerek her durumda senkronizasyonun sağlandığı gösterilmiştir.

Keywords

• Kesir dereceli sistemler
• Senkronizasyon
• Hiperkaos

FRACTIONAL ORDER ANALYSIS OF THE 4-DIMENSIONAL HYPERCHAOTIC PANG SYSTEM AND ITS ADAPTIVE SYNCHRONIZATION

Abstract

Fractional calculus is an effective method used to analyze the dynamics of nonlinear systems and provide more precise results. In this study, firstly, the 4-dimensional Pang system is introduced and its dynamic analyses demonstrating the hyperchaotic structure are given. Then, fractional-order calculations of the system are presented and the dynamics of the system for different fraction orders are investigated. At this point, according to the results obtained from Lyapunov exponents and phase-space representation, the Pang system exhibits periodic, chaotic, and hyperchaotic behaviors in different fractional orders. The results obtained at the end of this study present that the system is hyperchaotic for the fractional order of 3.52 and it is also confirmed that more accurate results are obtained than the integer-order analysis. In the next part of the study, adaptive synchronization of the fractional-order system is performed. Three different cases are examined and it is demonstrated that synchronization is achieved in all cases.

Keywords

• Fractional order systems
• Synchronization
• Hyperchaos

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