Research Article
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Synchronization of Gursey System

Year 2022, Volume: 26 Issue: 4, 813 - 819, 31.08.2022
https://doi.org/10.16984/saufenbilder.1059043

Abstract

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.

Supporting Institution

Istanbul University Scientific Research Projects Coordination Unit

Project Number

FBA-2018-28954.

References

  • [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.
Year 2022, Volume: 26 Issue: 4, 813 - 819, 31.08.2022
https://doi.org/10.16984/saufenbilder.1059043

Abstract

Project Number

FBA-2018-28954.

References

  • [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.
There are 26 citations in total.

Details

Primary Language English
Subjects Metrology, Applied and Industrial Physics
Journal Section Research Articles
Authors

Eren Tosyalı 0000-0001-9118-851X

Fatma Aydoğmuş 0000-0003-1434-2143

Project Number FBA-2018-28954.
Publication Date August 31, 2022
Submission Date January 17, 2022
Acceptance Date June 24, 2022
Published in Issue Year 2022 Volume: 26 Issue: 4

Cite

APA Tosyalı, E., & Aydoğmuş, F. (2022). Synchronization of Gursey System. Sakarya University Journal of Science, 26(4), 813-819. https://doi.org/10.16984/saufenbilder.1059043
AMA Tosyalı E, Aydoğmuş F. Synchronization of Gursey System. SAUJS. August 2022;26(4):813-819. doi:10.16984/saufenbilder.1059043
Chicago Tosyalı, Eren, and Fatma Aydoğmuş. “Synchronization of Gursey System”. Sakarya University Journal of Science 26, no. 4 (August 2022): 813-19. https://doi.org/10.16984/saufenbilder.1059043.
EndNote Tosyalı E, Aydoğmuş F (August 1, 2022) Synchronization of Gursey System. Sakarya University Journal of Science 26 4 813–819.
IEEE E. Tosyalı and F. Aydoğmuş, “Synchronization of Gursey System”, SAUJS, vol. 26, no. 4, pp. 813–819, 2022, doi: 10.16984/saufenbilder.1059043.
ISNAD Tosyalı, Eren - Aydoğmuş, Fatma. “Synchronization of Gursey System”. Sakarya University Journal of Science 26/4 (August 2022), 813-819. https://doi.org/10.16984/saufenbilder.1059043.
JAMA Tosyalı E, Aydoğmuş F. Synchronization of Gursey System. SAUJS. 2022;26:813–819.
MLA Tosyalı, Eren and Fatma Aydoğmuş. “Synchronization of Gursey System”. Sakarya University Journal of Science, vol. 26, no. 4, 2022, pp. 813-9, doi:10.16984/saufenbilder.1059043.
Vancouver Tosyalı E, Aydoğmuş F. Synchronization of Gursey System. SAUJS. 2022;26(4):813-9.