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Kesir Dereceli Hiperkaotik Osilatörlerde Trigonometrik Fonksiyon ile Çoklu Çeker Üretimi

Year 2021, Volume: 11 Issue: 4, 2673 - 2681, 15.12.2021
https://doi.org/10.21597/jist.969382

Abstract

Bu çalışmada, Sprott G sistemine doğrusal olmayan trigonometrik fonksiyonlar dahil edilerek kesir dereceli hiperkaotik çoklu çeker üretimi sunulmaktadır. İlk olarak, Sprott G sisteminin orijinal dinamik yapısının bilgisayar benzetimi ve Lyapunov üstelleri hesaplanmıştır. Daha sonra dinamik sistem, hiperkaotik çekerler üretmek için kesir dereceli analiz yöntemleri ile yeniden yapılandırılmıştır. Hiperkaotik yapısına ait benzetim çalışması ve nümerik analizi yapılmıştır. Son olarak, çoklu çeker yapıları oluşturmak için kesir dereceli hiperkaotik sisteme doğrusal olmayan trigonometrik fonksiyon serileri eklenmiştir. Önerilen sistemin dinamik davranışlarına ait bilgisayar benzetimi, faz uzay gösterimi, Lyapunov üstelleri analizi sunularak güvenilir haberleşme sistemleri için önemi açıklanmıştır.

References

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  • Alvarez G, Li S, 2006. Some basic cryptographic requirements for chaos-based cryptosystems. International journal of bifurcation and chaos, 16(08): 2129-2151.
  • Boccaletti S, Kurths J, Osipov G, Valladares DL, Zhou CS, 2002. The synchronization of chaotic systems. Physics reports, 366(1-2): 1-101.
  • Cafagna D, Grassi G, 2009. Hyperchaos in the fractional-order Rössler system with lowest-order. International Journal of Bifurcation and Chaos, 19(01): 339-347.
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  • Dadras S, Momeni HR, 2010. Four-scroll hyperchaos and four-scroll chaos evolved from a novel 4D nonlinear smooth autonomous system. Physics Letters A, 374(11-12): 1368-1373.
  • Gámez-Guzmán L, Cruz-Hernández C, López-Gutiérrez RM, Garcia-Guerrero EE, 2008. Synchronization of multi-scroll chaos generators: application to private communication. Revista Mexicana de Física, 54(4): 299-305.
  • Gámez-Guzmán L, Cruz-Hernández C, López-Gutiérrez RM, García-Guerrero EE, 2009. Synchronization of Chua’s circuits with multi-scroll attractors: application to communication. Communications in Nonlinear Science and Numerical Simulation, 14(6): 2765-2775.
  • Han F, Hu J, Yu X, Wang Y, 2007. Fingerprint images encryption via multi-scroll chaotic attractors. Applied Mathematics and Computation, 185(2): 931-939.
  • Kocarev L, 2001. Chaos-based cryptography: a brief overview. IEEE Circuits and Systems Magazine, 1(3): 6-21.
  • Lai Q, Wan Z, Kengne LK, Kuate PDK, Chen C, 2020. Two-memristor-based chaotic system with infinite coexisting attractors. IEEE Transactions on Circuits and Systems II: Express Briefs, 68(6): 2197-2201.
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  • Lü J, Chen G, 2006. Generating multiscroll chaotic attractors: theories, methods and applications. International Journal of Bifurcation and Chaos, 16(04): 775-858.
  • Lü J, Han F, Yu X, Chen G, 2004. Generating 3-D multi-scroll chaotic attractors: A hysteresis series switching method. Automatica, 40(10): 1677-1687.
  • Ma J, Wu X, Chu R, Zhang L, 2014. Selection of multi-scroll attractors in Jerk circuits and their verification using Pspice. Nonlinear Dynamics, 76(4): 1951-1962.
  • Matignon D, 1996. Stability results for fractional differential equations with applications to control processing. In Computational Engineering in Systems Applications, 2: 963-968.
  • Miller KS, Ross B, 1993. An introduction to the fractional calculus and fractional differential equations. Wiley.
  • Orue AB, Alvarez G, Pastor G, Romera M, Montoya F, Li S, 2010. A new parameter determination method for some double-scroll chaotic systems and its applications to chaotic cryptanalysis. Communications in Nonlinear Science and Numerical Simulation, 15(11): 3471-3483.
  • Pecora LM, Carroll TL, 1990. Synchronization in chaotic systems. Physical Review Letters, 64(8): 821.
  • Petráš I, Bednárová D, "Fractional - order chaotic systems", Emerging Technologies & Factory Automation 2009. ETFA 2009. IEEE Conference on, pp. 1-8, 2009.
  • Ross B, 1977. The development of fractional calculus 1695–1900. Historia Mathematica, 4(1): 75-89.
  • Rössler OE, 1976. An equation for continuous chaos. Physics Letters A, 57(5): 397-398.
  • Shilnikov LP, 1965. A case of the existence of a denumerable set of periodic motions. In Doklady Akademii Nauk, Russian Academy of Sciences,160: 558-561.
  • Si-Min Y, 2005. Circuit implementation for generating three-dimensional multi-scroll chaotic attractors via triangular wave series [J]. Acta Physica Sinica, 4.
  • Tang WK, Zhong GQ, Chen G, Man KF, 2001. Generation of n-scroll attractors via sine function. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 48(11):1369-72.
  • Yalçin ME, 2007. Multi-scroll and hypercube attractors from a general jerk circuit using Josephson junctions. Chaos, Solitons & Fractals, 34(5): 1659-1666.
  • Yang F, Mou J, Liu J, Ma C, Yan H, 2020. Characteristic analysis of the fractional-order hyperchaotic complex system and its image encryption application. Signal Processing, 169, 107373.
  • Yu F, Shen H, Zhang Z, Huang Y, Cai S, Du S, 2021. A new multi-scroll Chua’s circuit with composite hyperbolic tangent-cubic nonlinearity: Complex dynamics, Hardware implementation and Image encryption application. Integration.

Generation of Multi Scroll Attractor with Trigonometric Function in Fractional-Order Hyperchaotic Oscillators

Year 2021, Volume: 11 Issue: 4, 2673 - 2681, 15.12.2021
https://doi.org/10.21597/jist.969382

Abstract

In this study, fractional-order hyper chaotic multi-scroll generation is presented by incorporating nonlinear time delay functions into the Sprott G system. First, the computer simulation of the original dynamic structure of the Sprott G system and the Lyapunov exponents are calculated. Then the dynamic system is reconstructed with fractional analysis methods to produce hyper chaotic attractors. A simulation study and numerical analysis of the hyper chaotic structure were made. Finally, nonlinear trigonometric functions and time-delayed feedback function series are added to the fractional hyper chaotic system to create multi-scroll attractor structures. The computer simulation phase space representation of the dynamic behavior of the proposed system and the analysis of Lyapunov exponents are presented and its importance for reliable communication systems is explained.

References

  • Ai X, Sun K, He S, Wang H, 2015. Design of grid multiscroll chaotic attractors via transformations. International Journal of Bifurcation and Chaos, 25(10): 1530027.
  • Alvarez G, Li S, 2006. Some basic cryptographic requirements for chaos-based cryptosystems. International journal of bifurcation and chaos, 16(08): 2129-2151.
  • Boccaletti S, Kurths J, Osipov G, Valladares DL, Zhou CS, 2002. The synchronization of chaotic systems. Physics reports, 366(1-2): 1-101.
  • Cafagna D, Grassi G, 2009. Hyperchaos in the fractional-order Rössler system with lowest-order. International Journal of Bifurcation and Chaos, 19(01): 339-347.
  • Caponetto R, Dongola G, Maione G, Pisano A, 2014. Integrated technology fractional order proportional-integral-derivative design. Journal of Vibration and Control, 20(7): 1066-1075.
  • Charef A, Sun HH, Tsao YY, Onaral B, 1992. Fractal system as represented by singularity function. IEEE Transactions on automatic Control, 37(9): 1465-1470.
  • Dadras S, Momeni HR, 2010. Four-scroll hyperchaos and four-scroll chaos evolved from a novel 4D nonlinear smooth autonomous system. Physics Letters A, 374(11-12): 1368-1373.
  • Gámez-Guzmán L, Cruz-Hernández C, López-Gutiérrez RM, Garcia-Guerrero EE, 2008. Synchronization of multi-scroll chaos generators: application to private communication. Revista Mexicana de Física, 54(4): 299-305.
  • Gámez-Guzmán L, Cruz-Hernández C, López-Gutiérrez RM, García-Guerrero EE, 2009. Synchronization of Chua’s circuits with multi-scroll attractors: application to communication. Communications in Nonlinear Science and Numerical Simulation, 14(6): 2765-2775.
  • Han F, Hu J, Yu X, Wang Y, 2007. Fingerprint images encryption via multi-scroll chaotic attractors. Applied Mathematics and Computation, 185(2): 931-939.
  • Kocarev L, 2001. Chaos-based cryptography: a brief overview. IEEE Circuits and Systems Magazine, 1(3): 6-21.
  • Lai Q, Wan Z, Kengne LK, Kuate PDK, Chen C, 2020. Two-memristor-based chaotic system with infinite coexisting attractors. IEEE Transactions on Circuits and Systems II: Express Briefs, 68(6): 2197-2201.
  • Lorenz EN, 1963. Deterministic nonperiodic flow. Journal of atmospheric sciences, 20(2), 130-141.
  • Lü J, Chen G, 2006. Generating multiscroll chaotic attractors: theories, methods and applications. International Journal of Bifurcation and Chaos, 16(04): 775-858.
  • Lü J, Han F, Yu X, Chen G, 2004. Generating 3-D multi-scroll chaotic attractors: A hysteresis series switching method. Automatica, 40(10): 1677-1687.
  • Ma J, Wu X, Chu R, Zhang L, 2014. Selection of multi-scroll attractors in Jerk circuits and their verification using Pspice. Nonlinear Dynamics, 76(4): 1951-1962.
  • Matignon D, 1996. Stability results for fractional differential equations with applications to control processing. In Computational Engineering in Systems Applications, 2: 963-968.
  • Miller KS, Ross B, 1993. An introduction to the fractional calculus and fractional differential equations. Wiley.
  • Orue AB, Alvarez G, Pastor G, Romera M, Montoya F, Li S, 2010. A new parameter determination method for some double-scroll chaotic systems and its applications to chaotic cryptanalysis. Communications in Nonlinear Science and Numerical Simulation, 15(11): 3471-3483.
  • Pecora LM, Carroll TL, 1990. Synchronization in chaotic systems. Physical Review Letters, 64(8): 821.
  • Petráš I, Bednárová D, "Fractional - order chaotic systems", Emerging Technologies & Factory Automation 2009. ETFA 2009. IEEE Conference on, pp. 1-8, 2009.
  • Ross B, 1977. The development of fractional calculus 1695–1900. Historia Mathematica, 4(1): 75-89.
  • Rössler OE, 1976. An equation for continuous chaos. Physics Letters A, 57(5): 397-398.
  • Shilnikov LP, 1965. A case of the existence of a denumerable set of periodic motions. In Doklady Akademii Nauk, Russian Academy of Sciences,160: 558-561.
  • Si-Min Y, 2005. Circuit implementation for generating three-dimensional multi-scroll chaotic attractors via triangular wave series [J]. Acta Physica Sinica, 4.
  • Tang WK, Zhong GQ, Chen G, Man KF, 2001. Generation of n-scroll attractors via sine function. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 48(11):1369-72.
  • Yalçin ME, 2007. Multi-scroll and hypercube attractors from a general jerk circuit using Josephson junctions. Chaos, Solitons & Fractals, 34(5): 1659-1666.
  • Yang F, Mou J, Liu J, Ma C, Yan H, 2020. Characteristic analysis of the fractional-order hyperchaotic complex system and its image encryption application. Signal Processing, 169, 107373.
  • Yu F, Shen H, Zhang Z, Huang Y, Cai S, Du S, 2021. A new multi-scroll Chua’s circuit with composite hyperbolic tangent-cubic nonlinearity: Complex dynamics, Hardware implementation and Image encryption application. Integration.
There are 29 citations in total.

Details

Primary Language Turkish
Subjects Electrical Engineering
Journal Section Elektrik Elektronik Mühendisliği / Electrical Electronic Engineering
Authors

Kenan Altun 0000-0001-7419-1901

Publication Date December 15, 2021
Submission Date July 12, 2021
Acceptance Date August 31, 2021
Published in Issue Year 2021 Volume: 11 Issue: 4

Cite

APA Altun, K. (2021). Kesir Dereceli Hiperkaotik Osilatörlerde Trigonometrik Fonksiyon ile Çoklu Çeker Üretimi. Journal of the Institute of Science and Technology, 11(4), 2673-2681. https://doi.org/10.21597/jist.969382
AMA Altun K. Kesir Dereceli Hiperkaotik Osilatörlerde Trigonometrik Fonksiyon ile Çoklu Çeker Üretimi. J. Inst. Sci. and Tech. December 2021;11(4):2673-2681. doi:10.21597/jist.969382
Chicago Altun, Kenan. “Kesir Dereceli Hiperkaotik Osilatörlerde Trigonometrik Fonksiyon Ile Çoklu Çeker Üretimi”. Journal of the Institute of Science and Technology 11, no. 4 (December 2021): 2673-81. https://doi.org/10.21597/jist.969382.
EndNote Altun K (December 1, 2021) Kesir Dereceli Hiperkaotik Osilatörlerde Trigonometrik Fonksiyon ile Çoklu Çeker Üretimi. Journal of the Institute of Science and Technology 11 4 2673–2681.
IEEE K. Altun, “Kesir Dereceli Hiperkaotik Osilatörlerde Trigonometrik Fonksiyon ile Çoklu Çeker Üretimi”, J. Inst. Sci. and Tech., vol. 11, no. 4, pp. 2673–2681, 2021, doi: 10.21597/jist.969382.
ISNAD Altun, Kenan. “Kesir Dereceli Hiperkaotik Osilatörlerde Trigonometrik Fonksiyon Ile Çoklu Çeker Üretimi”. Journal of the Institute of Science and Technology 11/4 (December 2021), 2673-2681. https://doi.org/10.21597/jist.969382.
JAMA Altun K. Kesir Dereceli Hiperkaotik Osilatörlerde Trigonometrik Fonksiyon ile Çoklu Çeker Üretimi. J. Inst. Sci. and Tech. 2021;11:2673–2681.
MLA Altun, Kenan. “Kesir Dereceli Hiperkaotik Osilatörlerde Trigonometrik Fonksiyon Ile Çoklu Çeker Üretimi”. Journal of the Institute of Science and Technology, vol. 11, no. 4, 2021, pp. 2673-81, doi:10.21597/jist.969382.
Vancouver Altun K. Kesir Dereceli Hiperkaotik Osilatörlerde Trigonometrik Fonksiyon ile Çoklu Çeker Üretimi. J. Inst. Sci. and Tech. 2021;11(4):2673-81.