TY - JOUR T1 - FRACTIONAL ORDER ANALYSIS OF THE 4-DIMENSIONAL HYPERCHAOTIC PANG SYSTEM AND ITS ADAPTIVE SYNCHRONIZATION TT - 4-Boyutlu Hiperkaotik Pang Sisteminin Kesir Dereceli Analizi ve Adaptif Senkronizasyonu AU - Yılmaz, Gülnur AU - Günay, Enis PY - 2024 DA - April Y2 - 2024 DO - 10.17482/uumfd.1339620 JF - Uludağ Üniversitesi Mühendislik Fakültesi Dergisi JO - UUJFE PB - Bursa Uludağ Üniversitesi WT - DergiPark SN - 2148-4155 SP - 85 EP - 100 VL - 29 IS - 1 LA - en AB - 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. KW - Fractional order systems KW - Synchronization KW - Hyperchaos N2 - 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. CR - 1. Abd El-Maksoud, A. J., Abd El-Kader, A. A., Hassan, B. G., Rihan, N. G., Tolba, M. F., Said, L. A., Radwan, A. G., & Abu-Elyazeed, M. F. (2019). FPGA implementation of sound encryption system based on fractional-order chaotic systems. 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