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Control of New Type of Fractional Chaos Synchronization

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Book cover Proceedings of the International Conference on Advanced Intelligent Systems and Informatics 2017 (AISI 2017)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 639))

Abstract

Based on stability theory of linear fractional order systems and stability theory of linear integer order systems, the problem of coexistence of various types of synchronization between different dimensional fractional chaotic systems is investigated in this paper. Numerical and simulation results have clearly shown the effectiveness of the novel approach developed herein.

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References

  1. Azar, A.T., Vaidyanathan, S.: Advances in Chaos Theory and Intelligent Control, vol. 337. Springer, Berlin (2016)

    Book  MATH  Google Scholar 

  2. Azar, A.T., Vaidyanathan, S., Ouannas, A.: Fractional Order Control and Synchronization of Chaotic Systems. Studies in Computational Intelligence, vol. 688. Springer, Berlin (2017)

    Book  MATH  Google Scholar 

  3. Azar, A.T., Volos, C., Gerodimos, N.A., Tombras, G.S., Pham, V.T., Radwan, A.G., Vaidyanathan, S., Ouannas, A., Munoz-Pacheco, J.M.: A novel chaotic system without equilibrium: dynamics, synchronization, and circuit realization. Complexity, Article ID 7871467, 11 pages (2017)

    Google Scholar 

  4. Caputo, M.: Linear models of dissipation whose q is almost frequency independent-ii. Geophys. J. R. Astron. Soc. 13(5), 529–539 (1967)

    Article  Google Scholar 

  5. Chen, H., Chen, W., Zhang, B., Cao, H.: Robust synchronization of incommensurate fractional-order chaotic systems via second-order sliding mode technique. J. Appl. Math., Article ID 321253, 11 pages (2013)

    Google Scholar 

  6. Chun-Lai, L., Mei, Z., Feng, Z., Xuan-Bing, Y.: Projective synchronization for a fractional-order chaotic system via single sinusoidal coupling. Optik - Int. J. Light Electron Opt. 127(5), 2830–2836 (2016)

    Article  Google Scholar 

  7. Li, C.L., Wu, L.: Sliding mode control for synchronization of fractional permanent magnet synchronous motors with finite time. Optik - Int. J. Light Electron Opt. 127(6), 3329–3332 (2016)

    Article  Google Scholar 

  8. Liu, C., Liu, T., Liu, L., Liu, K.: A new chaotic attractor. Chaos, Solitons Fractals 22(5), 1031–1038 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  9. Martínex-Guerra, R., Mata-Machuca, J.L.: Fractional generalized synchronization in a class of nonlinear fractional order systems. Nonlinear Dyn. 77(4), 1237–1244 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  10. Matignon, D.: Stability results for fractional differential equations with applications to control processing. In: Proceedings of the IMACS Multiconference on Computational Engineering in Systems Applications, pp. 963–968 (1996)

    Google Scholar 

  11. Muthukumar, P., Balasubramaniam, P.: Feedback synchronization of the fractional order reverse butterfly-shaped chaotic system and its applicationto digital cryptography. Nonlinear Dyn. 74, 1169–1181 (2013)

    Article  MATH  Google Scholar 

  12. Ouannas, A., Grassi, G.: A new approach to study the coexistence of some synchronization types between chaotic maps with different dimensions. Nonlinear Dyn. 86(2), 1319–1328 (2016)

    Article  MATH  Google Scholar 

  13. Ouannas, A., Al-sawalha, M.M., Ziar, T.: Fractional chaos synchronization schemes for different dimensional systems with non-identical fractional-orders via two scaling matrices. Optik - Int. J. Light Electron Opt. 127(20), 8410–8418 (2016)

    Article  Google Scholar 

  14. Ouannas, A., Azar, A.T., Abu-Saris, R.: A new type of hybrid synchronization between arbitrary hyperchaotic maps. Int. J. Mach. Learn. Cybern., 1–8 (2016), http://dx.doi.org/10.1007/s13042-016-0566-3

  15. Ouannas, A., Azar, A.T., Vaidyanathan, S.: A robust method for new fractional hybrid chaos synchronization. Math. Methods Appl. Sci. 30(5), 1804–1812 (2016)

    MathSciNet  MATH  Google Scholar 

  16. Ouannas, A., Azar, A.T., Vaidyanathan, S.: New hybrid synchronization schemes based on coexistence of various types of synchronization between master-slave hyperchaotic systems. Int. J. Comput. Appl. Technol. 55(2), 112–120 (2017)

    Article  Google Scholar 

  17. Ouannas, A., Azar, A.T., Vaidyanathan, S.: On a simple approach for q-s synchronization of chaotic dynamical systems in continuous-time. Int. J. Comput. Sci. Math. 8(1), 20–27 (2017)

    Article  MathSciNet  Google Scholar 

  18. Ouannas, A., Azar, A.T., Ziar, T., Vaidyanathan, S.: Fractional inverse generalized chaos synchronization between different dimensional systems. In: Azar, A.T., Vaidyanathan, S., Ouannas, A. (eds.) Fractional Order Control and Synchronization of Chaotic Systems, pp. 525–551. Springer, Cham (2017)

    Chapter  Google Scholar 

  19. Ouannas, A., Azar, A.T., Ziar, T., Vaidyanathan, S.: A new method to synchronize fractional chaotic systems with different dimensions. In: Azar, A.T., Vaidyanathan, S., Ouannas, A. (eds.) Fractional Order Control and Synchronization of Chaotic Systems, pp. 581–611. Springer, Cham (2017), doi:10.1007/978-3-319-50249-6_20

  20. Pham, V.T., Vaidyanathan, S., Volos, C.K., Azar, A.T., Hoang, T.M., Van Yem, V.: A three-dimensional no-equilibrium chaotic system: Analysis, synchronization and its fractional order form. In: Azar, A.T., Vaidyanathan, S., Ouannas, A. (eds.) Fractional Order Control and Synchronization of Chaotic Systems, pp. 449–470. Springer, Cham (2017)

    Chapter  Google Scholar 

  21. Si, G., Sun, Z., Zhang, Y., Chen, W.: Projective synchronization of different fractional-order chaotic systems with non-identical orders. Nonlinear Anal. Real World Appl. 13(4), 1761–1771 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  22. Vaidyanathan, S., Azar, A.T., Ouannas, A.: An eight-term 3-D novel chaotic system with three quadratic nonlinearities, its adaptive feedback control and synchronization. In: Azar, A.T., Vaidyanathan, S., Ouannas, A. (eds.) Fractional Order Control and Synchronization of Chaotic Systems, pp. 719–746. Springer, Cham (2017)

    Chapter  Google Scholar 

  23. Vaidyanathan, S., Azar, A.T., Ouannas, A.: Hyperchaos and adaptive control of a novel hyperchaotic system with two quadratic nonlinearities. In: Azar, A.T., Vaidyanathan, S., Ouannas, A. (eds.) Fractional Order Control and Synchronization of Chaotic Systems, pp. 773–803. Springer, Cham (2017)

    Chapter  Google Scholar 

  24. Vaidyanathan, S., Zhu, Q., Azar, A.T.: Adaptive control of a novel nonlinear double convection chaotic system. In: Azar, A.T., Vaidyanathan, S., Ouannas, A. (eds.) Fractional Order Control and Synchronization of Chaotic Systems, pp. 357–385. Springer, Cham (2017)

    Chapter  Google Scholar 

  25. Wang, Z., Volos, C., Kingni, S.T., Azar, A.T., Pham, V.T.: Four-wing attractors in a novel chaotic system with hyperbolic sine nonlinearity. Optik - Int. J. Light Electron Opt. 131, 1071–1078 (2017)

    Article  Google Scholar 

  26. Xi, H., Li, Y., Huang, X.: Adaptive function projective combination synchronization of three different fractional-order chaotic systems. Optik - Int. J. Light Electron Opt. 126(24), 5346–5349 (2015)

    Article  Google Scholar 

  27. Yi, C., Liping, C., Ranchao, W., Juan, D.: Q-S synchronization of the fractional-order unified system. Pramana 80(3), 449–461 (2013)

    Article  Google Scholar 

  28. Zhang, L., Liu, T.: Full state hybrid projective synchronization of variable-order fractional chaotic/hyperchaotic systems with nonlinear external disturbances and unknown parameters. J. Nonlinear Sci. Appl. 9(3), 1064–1076 (2016)

    MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Faculty of Computers and Information, Benha University, Banha, Egypt

    Ahmad Taher Azar

  2. Nile University, 6th of October City, Egypt

    Ahmad Taher Azar

  3. Laboratory of Mathematics, Informatics and Systems (LAMIS), University of Larbi Tebessi, 12002, Tebessa, Algeria

    Adel Ouannas

  4. Faculty of Natural Sciences, Jamia Millia Islamia, New Delhi, India

    Shikha Singh

Authors
  1. Ahmad Taher Azar
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  2. Adel Ouannas
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  3. Shikha Singh
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Corresponding author

Correspondence to Ahmad Taher Azar .

Editor information

Editors and Affiliations

  1. Faculty of Computers and Information, Information Technology Department, Cairo University, Giza, Egypt

    Aboul Ella Hassanien

  2. Dubai International Academic City, The British University in Dubai, Dubai, United Arab Emirates

    Khaled Shaalan

  3. Faculty of Computers and Informatics, Suez Canal University, Ismailia, Egypt

    Tarek Gaber

  4. Ain Shams University, Cairo, Egypt

    Mohamed F. Tolba

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Azar, A.T., Ouannas, A., Singh, S. (2018). Control of New Type of Fractional Chaos Synchronization. In: Hassanien, A., Shaalan, K., Gaber, T., Tolba, M. (eds) Proceedings of the International Conference on Advanced Intelligent Systems and Informatics 2017. AISI 2017. Advances in Intelligent Systems and Computing, vol 639. Springer, Cham. https://doi.org/10.1007/978-3-319-64861-3_5

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  • DOI: https://doi.org/10.1007/978-3-319-64861-3_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-64860-6

  • Online ISBN: 978-3-319-64861-3

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