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

Yıl 2024, Cilt: 29 Sayı: 1, 85 - 100, 22.04.2024

Gülnur Yılmaz Enis Günay

https://doi.org/10.17482/uumfd.1339620

Öz

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.

Anahtar Kelimeler

Kesir dereceli sistemler Senkronizasyon Hiperkaos

Kaynakça

  • 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. Microelectronics Journal, 90, 323–335. https://doi.org/10.1016/j.mejo.2019.05.005
  • 2. Al-Obeidi, A. S., & AL-Azzawi, S. F. (2019). Projective synchronization for a cass of 6-D hyperchaotic lorenz system. Indonesian Journal of Electrical Engineering and Computer Science, 16(2), 692– 700. https://doi.org/10.11591/IJEECS.V16.I2.PP692-700
  • 3. Bouridah, M. S., Bouden, T., & Yalçin, M. E. (2021). Delayed outputs fractional-order hyperchaotic systems synchronization for images encryption. Multimedia Tools and Applications 2021 80:10, 80(10), 14723–14752. https://doi.org/10.1007/S11042-020-10425-3
  • 4. Caputo, M. (1967). Linear Models of Dissipation whose Q is almost Frequency Independent—II. Geophysical Journal International, 13(5), 529–539. https://doi.org/10.1111/J.1365-246X.1967.TB02303.X
  • 5. Gularte, K. H. M., Alves, L. M., Vargas, J. A. R., Alfaro, S. C. A., De Carvalho, G. C., & Romero, J. F. A. (2021). Secure Communication Based on Hyperchaotic Underactuated Projective Synchronization. IEEE Access, 9, 166117–166128. https://doi.org/10.1109/ACCESS.2021.3134829
  • 6. Huang, W., Jiang, D., An, Y., Liu, L., & Wang, X. (2021). A Novel Double-Image Encryption Algorithm Based on Rossler Hyperchaotic System and Compressive Sensing. IEEE Access, 9, 41704–41716. https://doi.org/10.1109/ACCESS.2021.3065453
  • 7. Liao, T. L., Wan, P. Y., & Yan, J. J. (2022). Design and synchronization of chaos-based true random number generators and its FPGA implementation. IEEE Access. https://doi.org/10.1109/ACCESS.2022.3142536
  • 8. Lin, L., Wang, Q., & Cai, G. (2022). FPGA Realization of Two Different Fractional- Order Time-Delay Chaotic System With Predefined Synchronization Time. IEEE Access, 10, 133663–133672. https://doi.org/10.1109/ACCESS.2022.3231610
  • 9. Lin, L., Wang, Q., He, B., Chen, Y., Peng, X., & Mei, R. (2021). Adaptive predefined-time synchronization of two different fractional-order chaotic systems with time-delay. IEEE Access, 9, 31908–31920. https://doi.org/10.1109/ACCESS.2021.3059324
  • 10. Lorenz, E. N. (1963). Deterministic Nonperiodic Flow. Journal of the Atmospheric Sciences, 20(2), 130–141. https://doi.org/10.1175/1520-0469(1963)020<0130:dnf>2.0.co;2
  • 11. Lu, J. G. (2006). Chaotic dynamics of the fractional-order Lü system and its synchronization. Physics Letters A, 354(4), 305–311. https://doi.org/10.1016/J.PHYSLETA.2006.01.068
  • 12. Meng, X., Wu, Z., Gao, C., Jiang, B., & Karimi, H. R. (2021). Finite-time projective synchronization control of variable-order fractional chaotic systems via sliding mode approach. IEEE Transactions on Circuits and Systems II: Express Briefs, 68(7), 2503–2507. https://doi.org/10.1109/TCSII.2021.3055753
  • 13. Nwachioma, C., & Pérez-Cruz, J. H. (2021). Analysis of a new chaotic system, electronic realization and use in navigation of differential drive mobile robot. Chaos, Solitons and Fractals, 144, 110684. https://doi.org/10.1016/J.CHAOS.2021.110684
  • 14. Oldham, K. B., & Spanier, J. (1974). The fractional calculus : theory and applications of differentiation and integration to arbitrary order. 234.
  • 15. Pang, S., & Liu, Y. (2011). A new hyperchaotic system from the Lü system and its control. Journal of Computational and Applied Mathematics, 235(8), 2775–2789. https://doi.org/10.1016/j.cam.2010.11.029
  • 16. Pecora, L. M., Carroll, T. L., Johnson, G. A., Mar, D. J., & Heagy, J. F. (1997). Fundamentals of synchronization in chaotic systems, concepts, and applications. Chaos, 7(4), 520–543. https://doi.org/10.1063/1.166278
  • 17. Qammer, H. K. (1995). Chaos in a Fractional Order Chua’s System. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 42(8), 485–490. https://doi.org/10.1109/81.404062
  • 18. Sajjadi, S. S., Baleanu, D., Jajarmi, A., & Pirouz, H. M. (2020). A new adaptive synchronization and hyperchaos control of a biological snap oscillator. Chaos, Solitons and Fractals, 138. https://doi.org/10.1016/j.chaos.2020.109919
  • 19. Scherer, R., Kalla, S. L., Tang, Y., & Huang, J. (2011). The Grünwald–Letnikov method for fractional differential equations. Computers & Mathematics with Applications, 62(3), 902–917. https://doi.org/10.1016/J.CAMWA.2011.03.054
  • 20. Singh, S., Han, S., & Lee, S. M. (2021). Adaptive single input sliding mode control for hybrid-synchronization of uncertain hyperchaotic Lu systems. Journal of the Franklin Institute. https://doi.org/10.1016/J.JFRANKLIN.2021.07.037
  • 21. Vaidyanathan, S., Sambas, A., Mujiarto, Mamat, M., Wilarso, Mada Sanjaya, W. S., Sutoni, A., & Gunawan, I. (2021). A New 4-D Multistable Hyperchaotic Two-Scroll System, its Bifurcation Analysis, Synchronization and Circuit Simulation. Journal of Physics: Conference Series, 1764(1). https://doi.org/10.1088/1742-6596/1764/1/012206
  • 22. Wang, F., Wang, R., Iu, H. H. C., Liu, C., & Fernando, T. (2019). A Novel Multi-Shape Chaotic Attractor and Its FPGA Implementation. IEEE Transactions on Circuits and Systems II: Express Briefs, 66(12), 2062–2066. https://doi.org/10.1109/TCSII.2019.2907709
  • 23. Wang, J., Yu, W., Wang, J., Zhao, Y., Zhang, J., & Jiang, D. (2019). A new six-dimensional hyperchaotic system and its secure communication circuit implementation. International Journal of Circuit Theory and Applications, 47(5), 702–717. https://doi.org/10.1002/CTA.2617
  • 24. Wang, P., Wen, G., Yu, X., Yu, W., & Huang, T. (2019). Synchronization of multi-layer networks: From node-to-node synchronization to complete synchronization. IEEE Transactions on Circuits and Systems I: Regular Papers, 66(3), 1141–1152. https://doi.org/10.1109/TCSI.2018.2877414
  • 25. Wang, S., Hong, L., Jiang, J., & Li, X. (2020). Synchronization precision analysis of a fractional-order hyperchaos with application to image encryption. AIP Advances, 10(10). https://doi.org/10.1063/5.0012493
  • 26. Wu, X., Lu, H., & Shen, S. (2009). Synchronization of a new fractional-order hyperchaotic system. Physics Letters, Section A: General, Atomic and Solid State Physics, 373(27–28), 2329–2337. https://doi.org/10.1016/j.physleta.2009.04.063
  • 27. Yılmaz, G., Altun, K., & Günay, E. (2022). Synchronization of hyperchaotic Wang-Liu system with experimental implementation on FPAA and FPGA. Analog Integrated Circuits and Signal Processing, 113(2), 145–161. https://doi.org/10.1007/S10470-022-02073-4

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

Yıl 2024, Cilt: 29 Sayı: 1, 85 - 100, 22.04.2024

Gülnur Yılmaz Enis Günay

https://doi.org/10.17482/uumfd.1339620

Öz

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.

Anahtar Kelimeler

Fractional order systems Synchronization Hyperchaos

Kaynakça

  • 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. Microelectronics Journal, 90, 323–335. https://doi.org/10.1016/j.mejo.2019.05.005
  • 2. Al-Obeidi, A. S., & AL-Azzawi, S. F. (2019). Projective synchronization for a cass of 6-D hyperchaotic lorenz system. Indonesian Journal of Electrical Engineering and Computer Science, 16(2), 692– 700. https://doi.org/10.11591/IJEECS.V16.I2.PP692-700
  • 3. Bouridah, M. S., Bouden, T., & Yalçin, M. E. (2021). Delayed outputs fractional-order hyperchaotic systems synchronization for images encryption. Multimedia Tools and Applications 2021 80:10, 80(10), 14723–14752. https://doi.org/10.1007/S11042-020-10425-3
  • 4. Caputo, M. (1967). Linear Models of Dissipation whose Q is almost Frequency Independent—II. Geophysical Journal International, 13(5), 529–539. https://doi.org/10.1111/J.1365-246X.1967.TB02303.X
  • 5. Gularte, K. H. M., Alves, L. M., Vargas, J. A. R., Alfaro, S. C. A., De Carvalho, G. C., & Romero, J. F. A. (2021). Secure Communication Based on Hyperchaotic Underactuated Projective Synchronization. IEEE Access, 9, 166117–166128. https://doi.org/10.1109/ACCESS.2021.3134829
  • 6. Huang, W., Jiang, D., An, Y., Liu, L., & Wang, X. (2021). A Novel Double-Image Encryption Algorithm Based on Rossler Hyperchaotic System and Compressive Sensing. IEEE Access, 9, 41704–41716. https://doi.org/10.1109/ACCESS.2021.3065453
  • 7. Liao, T. L., Wan, P. Y., & Yan, J. J. (2022). Design and synchronization of chaos-based true random number generators and its FPGA implementation. IEEE Access. https://doi.org/10.1109/ACCESS.2022.3142536
  • 8. Lin, L., Wang, Q., & Cai, G. (2022). FPGA Realization of Two Different Fractional- Order Time-Delay Chaotic System With Predefined Synchronization Time. IEEE Access, 10, 133663–133672. https://doi.org/10.1109/ACCESS.2022.3231610
  • 9. Lin, L., Wang, Q., He, B., Chen, Y., Peng, X., & Mei, R. (2021). Adaptive predefined-time synchronization of two different fractional-order chaotic systems with time-delay. IEEE Access, 9, 31908–31920. https://doi.org/10.1109/ACCESS.2021.3059324
  • 10. Lorenz, E. N. (1963). Deterministic Nonperiodic Flow. Journal of the Atmospheric Sciences, 20(2), 130–141. https://doi.org/10.1175/1520-0469(1963)020<0130:dnf>2.0.co;2
  • 11. Lu, J. G. (2006). Chaotic dynamics of the fractional-order Lü system and its synchronization. Physics Letters A, 354(4), 305–311. https://doi.org/10.1016/J.PHYSLETA.2006.01.068
  • 12. Meng, X., Wu, Z., Gao, C., Jiang, B., & Karimi, H. R. (2021). Finite-time projective synchronization control of variable-order fractional chaotic systems via sliding mode approach. IEEE Transactions on Circuits and Systems II: Express Briefs, 68(7), 2503–2507. https://doi.org/10.1109/TCSII.2021.3055753
  • 13. Nwachioma, C., & Pérez-Cruz, J. H. (2021). Analysis of a new chaotic system, electronic realization and use in navigation of differential drive mobile robot. Chaos, Solitons and Fractals, 144, 110684. https://doi.org/10.1016/J.CHAOS.2021.110684
  • 14. Oldham, K. B., & Spanier, J. (1974). The fractional calculus : theory and applications of differentiation and integration to arbitrary order. 234.
  • 15. Pang, S., & Liu, Y. (2011). A new hyperchaotic system from the Lü system and its control. Journal of Computational and Applied Mathematics, 235(8), 2775–2789. https://doi.org/10.1016/j.cam.2010.11.029
  • 16. Pecora, L. M., Carroll, T. L., Johnson, G. A., Mar, D. J., & Heagy, J. F. (1997). Fundamentals of synchronization in chaotic systems, concepts, and applications. Chaos, 7(4), 520–543. https://doi.org/10.1063/1.166278
  • 17. Qammer, H. K. (1995). Chaos in a Fractional Order Chua’s System. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 42(8), 485–490. https://doi.org/10.1109/81.404062
  • 18. Sajjadi, S. S., Baleanu, D., Jajarmi, A., & Pirouz, H. M. (2020). A new adaptive synchronization and hyperchaos control of a biological snap oscillator. Chaos, Solitons and Fractals, 138. https://doi.org/10.1016/j.chaos.2020.109919
  • 19. Scherer, R., Kalla, S. L., Tang, Y., & Huang, J. (2011). The Grünwald–Letnikov method for fractional differential equations. Computers & Mathematics with Applications, 62(3), 902–917. https://doi.org/10.1016/J.CAMWA.2011.03.054
  • 20. Singh, S., Han, S., & Lee, S. M. (2021). Adaptive single input sliding mode control for hybrid-synchronization of uncertain hyperchaotic Lu systems. Journal of the Franklin Institute. https://doi.org/10.1016/J.JFRANKLIN.2021.07.037
  • 21. Vaidyanathan, S., Sambas, A., Mujiarto, Mamat, M., Wilarso, Mada Sanjaya, W. S., Sutoni, A., & Gunawan, I. (2021). A New 4-D Multistable Hyperchaotic Two-Scroll System, its Bifurcation Analysis, Synchronization and Circuit Simulation. Journal of Physics: Conference Series, 1764(1). https://doi.org/10.1088/1742-6596/1764/1/012206
  • 22. Wang, F., Wang, R., Iu, H. H. C., Liu, C., & Fernando, T. (2019). A Novel Multi-Shape Chaotic Attractor and Its FPGA Implementation. IEEE Transactions on Circuits and Systems II: Express Briefs, 66(12), 2062–2066. https://doi.org/10.1109/TCSII.2019.2907709
  • 23. Wang, J., Yu, W., Wang, J., Zhao, Y., Zhang, J., & Jiang, D. (2019). A new six-dimensional hyperchaotic system and its secure communication circuit implementation. International Journal of Circuit Theory and Applications, 47(5), 702–717. https://doi.org/10.1002/CTA.2617
  • 24. Wang, P., Wen, G., Yu, X., Yu, W., & Huang, T. (2019). Synchronization of multi-layer networks: From node-to-node synchronization to complete synchronization. IEEE Transactions on Circuits and Systems I: Regular Papers, 66(3), 1141–1152. https://doi.org/10.1109/TCSI.2018.2877414
  • 25. Wang, S., Hong, L., Jiang, J., & Li, X. (2020). Synchronization precision analysis of a fractional-order hyperchaos with application to image encryption. AIP Advances, 10(10). https://doi.org/10.1063/5.0012493
  • 26. Wu, X., Lu, H., & Shen, S. (2009). Synchronization of a new fractional-order hyperchaotic system. Physics Letters, Section A: General, Atomic and Solid State Physics, 373(27–28), 2329–2337. https://doi.org/10.1016/j.physleta.2009.04.063
  • 27. Yılmaz, G., Altun, K., & Günay, E. (2022). Synchronization of hyperchaotic Wang-Liu system with experimental implementation on FPAA and FPGA. Analog Integrated Circuits and Signal Processing, 113(2), 145–161. https://doi.org/10.1007/S10470-022-02073-4
Toplam 27 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Elektronik
Bölüm Araştırma Makaleleri
Yazarlar

Gülnur Yılmaz 0000-0001-8940-7883

Enis Günay 0000-0002-0447-6810

Erken Görünüm Tarihi 28 Mart 2024
Yayımlanma Tarihi 22 Nisan 2024
Gönderilme Tarihi 9 Ağustos 2023
Kabul Tarihi 9 Ocak 2024
Yayımlandığı Sayı Yıl 2024 Cilt: 29 Sayı: 1

Kaynak Göster

APA Yılmaz, G., & Günay, E. (2024). FRACTIONAL ORDER ANALYSIS OF THE 4-DIMENSIONAL HYPERCHAOTIC PANG SYSTEM AND ITS ADAPTIVE SYNCHRONIZATION. Uludağ Üniversitesi Mühendislik Fakültesi Dergisi, 29(1), 85-100. https://doi.org/10.17482/uumfd.1339620
AMA Yılmaz G, Günay E. FRACTIONAL ORDER ANALYSIS OF THE 4-DIMENSIONAL HYPERCHAOTIC PANG SYSTEM AND ITS ADAPTIVE SYNCHRONIZATION. UUJFE. Nisan 2024;29(1):85-100. doi:10.17482/uumfd.1339620
Chicago Yılmaz, Gülnur, ve Enis Günay. “FRACTIONAL ORDER ANALYSIS OF THE 4-DIMENSIONAL HYPERCHAOTIC PANG SYSTEM AND ITS ADAPTIVE SYNCHRONIZATION”. Uludağ Üniversitesi Mühendislik Fakültesi Dergisi 29, sy. 1 (Nisan 2024): 85-100. https://doi.org/10.17482/uumfd.1339620.
EndNote Yılmaz G, Günay E (01 Nisan 2024) FRACTIONAL ORDER ANALYSIS OF THE 4-DIMENSIONAL HYPERCHAOTIC PANG SYSTEM AND ITS ADAPTIVE SYNCHRONIZATION. Uludağ Üniversitesi Mühendislik Fakültesi Dergisi 29 1 85–100.
IEEE G. Yılmaz ve E. Günay, “FRACTIONAL ORDER ANALYSIS OF THE 4-DIMENSIONAL HYPERCHAOTIC PANG SYSTEM AND ITS ADAPTIVE SYNCHRONIZATION”, UUJFE, c. 29, sy. 1, ss. 85–100, 2024, doi: 10.17482/uumfd.1339620.
ISNAD Yılmaz, Gülnur - Günay, Enis. “FRACTIONAL ORDER ANALYSIS OF THE 4-DIMENSIONAL HYPERCHAOTIC PANG SYSTEM AND ITS ADAPTIVE SYNCHRONIZATION”. Uludağ Üniversitesi Mühendislik Fakültesi Dergisi 29/1 (Nisan 2024), 85-100. https://doi.org/10.17482/uumfd.1339620.
JAMA Yılmaz G, Günay E. FRACTIONAL ORDER ANALYSIS OF THE 4-DIMENSIONAL HYPERCHAOTIC PANG SYSTEM AND ITS ADAPTIVE SYNCHRONIZATION. UUJFE. 2024;29:85–100.
MLA Yılmaz, Gülnur ve Enis Günay. “FRACTIONAL ORDER ANALYSIS OF THE 4-DIMENSIONAL HYPERCHAOTIC PANG SYSTEM AND ITS ADAPTIVE SYNCHRONIZATION”. Uludağ Üniversitesi Mühendislik Fakültesi Dergisi, c. 29, sy. 1, 2024, ss. 85-100, doi:10.17482/uumfd.1339620.
Vancouver Yılmaz G, Günay E. FRACTIONAL ORDER ANALYSIS OF THE 4-DIMENSIONAL HYPERCHAOTIC PANG SYSTEM AND ITS ADAPTIVE SYNCHRONIZATION. UUJFE. 2024;29(1):85-100.

DUYURU:

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