Synchronization of Gursey System

Yıl 2022, , 813 - 819, 31.08.2022

Eren Tosyalı , Fatma Aydoğmuş

https://doi.org/10.16984/saufenbilder.1059043

Öz

Gursey Model, the only possible four-dimensional pure spinor model, proposed as a possible basis for a unitary description of elementary particles. The model exhibits chaotic behaviors depending on the system parameter values. In this study, we investigate the synchronization of chaotic dynamic in the Gursey wave equation that has particle-like solutions derived classical field equations. Numerical results for synchronization of the Gursey system are performed to indicate the accuracy of the used method.

Anahtar Kelimeler

synchronization, Gursey, chaos

Destekleyen Kurum

Istanbul University Scientific Research Projects Coordination Unit

Proje Numarası

FBA-2018-28954.

Kaynakça

• [1] F. Gursey, “On a conform-invariant wave equation,” II Nuvovo Cimento, vol. 3, no. 5, pp. 998-1006, 1956.
• [2] F. Kortel, “On some solutions of Gursey’s conformal-invariant spinor wave eqution,” II Nuovo Cimento, vol. 4, no. 2 pp. 210-215, 1956.
• [3] C. Rebbi, G. Solliani, “Solitons and particles.” 1st edition, World Scientific, USA, pp. 792-811, 1984.
• [4] M. Soler, “Classical, Stable, Nonlinear Spinor Field with Positive Rest Energy,” Physical Review D, vol. 1, no.10, pp. 2766–2769, 1970.
• [5] S. Sağaltıcı, “Gürsey Solitonlarının Düzensiz Dinamik Yapılarının İncelenmesi,” M.S. thesis, Istanbul University, Departmrnt of Physics, Istanbul, Turkey, 2004.
• [6] S. Strogatz, “Nonlinear Dynamics and Chaos: With application to physics, biology, chemistry and engineering.”, 2nd edition, CRC Press , USA, pp. 423-448, 2018.
• [7] F. Aydogmus, E. Tosyalı, “Common Behaviors of Spinor-Type Instantons in 2D Thirring and 4D Gursey Fermionic Models,” vol. 2014, no.148375, pp. 0-11, 2014.
• [8] F. Aydogmus, “Chaos in a 4D dissipative nonlinear fermionic model,” International Journal of Modern Physics C, vol. 26, no. 7, pp. 1550083, 2015.
• [9] E. Tosyali, F. Aydogmus, “Soliton Solutions of Gursey Model With Bichromatic Force,” AIP Conference Preceeding Third International Conference Of Mathematical Sciences (ICMS 2019) pp. 56–59, 2019.
• [10] L. M. Pecora, T. L. Caroll, “Synchronization in chaotic systems,” Physical Review Letters, vol. 64, no. 8, pp. 821–824, 1990.
• [11] M. T. Yassen, “Chaos Synchronization Between Two Different Chaotic Systems Using Control”, Chaos, Solitons and Fractals, vol. 23, no. 1, pp. 31-140, 2004.
• [12] A. Ucar, K. E. Lonngren, E. Bai, “Synchronization of the unified chaotic systems via active control”, Chaos Solitons and Fractals, vol. 27, no. 5, pp. 1292-1297, 2006.
• [13] S. Oancea, F. Grosu, A. Lazar, I. Grosu, “Master–slave synchronization of Lorenz systems using a single controller”, Chaos, Solitons & Fractals, vol. 41, no. 5, pp. 2575-2580, 2009.
• [14] B. A. Idowu, U. E. Vincent, “Synchronization and Stabilization of Chaotic Dynamics in a Quasi-1D Bose-Einstein Condensate”, Journal of Chaos, vol. 2013, no.-, pp. 723581, 2013.
• [15] M. E., Yalcin, J. A. K. Suykens, J. P. L. Wandewalle, “Synchronization of Chaotic Lur'e Systems”, Cellular Neural Networks Multi-Scroll Chaos and Synchronization, 1st edition, World Scientific Series on Nonlinear Science, Series A., USA, pp. 105-154, 2013.
• [16] Q. Yang, “Stabilization and synchronization of Bose–Einstein condensate systems by single input linear controllers”, Complexity, vol. 141, no. -, pp. 66-71, 2017.
• [17] K. Ding, “Master-Slave Synchronization of Chaotic Φ6 Duffing Oscillators by Linear State Error Feedback Control”, Complexity, vol. 2019, no. 3637902, pp. 1-10, 2019.
• [18] E. Tosyali, F. Aydogmus, “Master-slave synchronization of Bose-Einstein condensate in 1D tilted bichromatical optical lattice,” Condensed Matter Physics, vol. 23, no. 1, pp. 13001, 2020.
• [19] E. A. Jackson, I. Grosu, “An open-plus-cloosed-loop (OPCL) control of complex dynamic systems” Physica D, vol. 85, pp. 1-9, 1995.
• [20] H. Du, “Adaptive Open-Plus-Closed-Loop Control Method of Modified Function Projective Synchronization In Complex Networks” International Journal of Modern Physics C, vol. 22, pp. 1393-1407, 2011.
• [21] E. A. Jackson, I. Grosu, “An open-plus-cloosed-loop Approach to Synchronization of Chaotic and Hyperchaotic Maps” International Journal of Bifurcation and Chaos , vol. 12, pp. 1219-1225, 2002.
• [22] W. Heisenberg, “Zur Quantentheorie nichtrenormierbarer Wellen-gleichungen,” Zeitschrift für Natuerforschung A, vol. 9, no. 84 pp. 292-303, 1954.
• [23] C. W. Wu, L. O. Chua, “A simple way to synchronize chaotic systems with applications to secure communication systems,” International Journal of Bifurcation and Chaos, vol. 3, no. 6 pp. 1619-1627, 1993.
• [24] I. Grosu, “Robust Synchronization,” Physical Review E, vol. 56, no. 3 pp. 3709-3712, 1997.
• [25] M. Sandri, “Numerical Calculation of Lyapunov exponents,” The Mathematica Journal, vol. 6, no. 3 pp. 78-84, 1996.
• [26] J. P. Singh, B. K. Roy, “The nature of Lyapunov exponent is (+,+,-,-). Is it a hyperchaotic system?,” Chaos Soliton & Fractals, vol. 92, no. - pp. 73-85, 2016.