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Combined modified function projective synchronization of different systems through adaptive control

Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This work describes a new study to achieve a combination of modified function projective synchronization between three different chaotic systems through adaptive control. Using the Lyapunov function theory, the asymptotic stability of the error dynamics is obtained and discussed. Further, we set some appropriate initial conditions for the state variables and assigning specific values to the parameters and obtain the graphical results, which shows the efficiencies of the new method. Finally, we summarized our work with conclusion and references.
Rocznik
Strony
133--146
Opis fizyczny
Bibliogr. 32 poz., rys., wykr., wzory
Twórcy
  • Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
  • Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
  • Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516
Bibliografia
  • [1] U. Cavusoglu, A. Akgul, A. Zengin and I. Pehlivan: The design and implementation of hybrid RSA algorithm using a novel chaos based RNG. Chaos, Solitons and Fractals, 104 (2017), 655–667.
  • [2] I. Bodale and V. A. Oancea: Chaos control for Willamowski-Rössle rmodel of chemical reactions. Chaos, Solitons and Fractals, 78 (2015), 1–9.
  • [3] E. M. Elabbasy and M. M. El-Dessoky: Adaptive feedback control for the projective synchronization for Lu dynamical system and application in secure communication. Chinese Journal of Physics, 48(6) (2010), 863–872.
  • [4] X. Xu: Generalized function projective synchronization of chaotic systems for secure communication. Advances in Signal Processing, 2011(1) (2011), 6180–6187.
  • [5] L. M. Pecora and T. L. Carroll: Synchronization in chaotic systems. Physical Review Letters, 64(8) (1990), 821–824.
  • [6] T. L. Carroll and L. M. Perora: Synchronizing a chaotic systems. IEEE Transactions on circuits and systems, 38(4) (1991), 453–456.
  • [7] N. Rulkov, M. Sushchik, L. Tsimring, and H. Abarbanel: Generalized synchronization of chaos in directionally coupled chaotic systems. Physical Review Letters, 51(2) (1995), 980–994.
  • [8] S. Yang and C. Duan: Generalized synchronization in chaotic systems. Chaos, Solitons and Fractals, 9(10) (1998), 1703–1707.
  • [9] X. Yang: A framework for synchronization theory. Chaos, Solitons and Fractals, 11(9) (2000), 1365–1368.
  • [10] E. Bai and K. Lonngren: Sequential synchronization of two Lorenz system using active control. Chaos, Solitons and Fractals, 11(7) (2000), 1041–1044.
  • [11] E. M. Elabbasy, H. N. Agiza, and M. M. El-Dessoky: Global chaos synchronization for four-scroll attractor by nonlinear control. Scientific Research and Essay, 1(3) (2006), 65–71.
  • [12] E. M. Elabbasy and M. M. El-Dessoky: Adaptive coupled synchronization of coupled chaotic dynamical systems. Applied Sciences Research, 2(2) (2007), 88–102.
  • [13] M. M. El-Dessoky: Synchronization and anti-synchronization of a hyperchaotic Chen system. Chaos, Solitons and Fractals, 39(4) (2009), 1790–1797.
  • [14] M. M. El-Dessoky: Anti-synchronization of four scroll attractor with fully unknown parameters. Nonlinear Analysis: Real World Applications, 11(2) (2010), 778–783.
  • [15] G. Li: Generalized synchronization of chaos based on suitable separation. Chaos, Solitons and Fractals, 39(5) (2009), 2056–2062.
  • [16] K. Ojo, S. Ogunjo, and A. Olagundoye: Projective synchronization via active control of identical chaotic oscillators with parametric and external excitation. International Journal of Nonlinear Science, 24(2) (2017), 76–83.
  • [17] E. M. Shahverdiev, S. Sivaprakasam, and K. A. Shore: Lag synchronization in time-delayed systems. Physics Letters A, 292 (2002), 320–324.
  • [18] R. Femat and G. Solis-Perales:On the chaos synchronization phenomena. Physics Letters A, 262 (1999), 50–60.
  • [19] R. Mainieri and J. Rehacek: Projective synchronization in three-dimensioned chaotic systems. Physical Review Letters, 82 (1999) 3042–3045.
  • [20] Y. Chen and X. Li: Function projective synchronization between two identical chaotic systems. International Journal of Modern Physics C, 18(5) (2007), 883–888.
  • [21] M. M. El-Dessoky, E. O. Alzahrany, and N. A. Almohammadi: Chaos Control and Function Projective Synchronization of Noval Chaotic Dynamical System. Computational Analysis and Applications, 27(1), (2019), 162–172.
  • [22] G. Li: Modified projective synchronization of chaotic system. Chaos, Solitons and Fractals, 32(5) (2007), 1786–1790.
  • [23] N. Cai, Y. Jing, and S. Zhang: Modified projective synchronization of chaotic systems with disturbances via active sliding mode control. Communications in Nonlinear Science and Numerical Simulation, 15(6) (2010), 1613–1620.
  • [24] S. Zheng, G. Dong, and Q. Bi: Adaptive modified function projective synchronization of hyperchaotic systems with unknown parameters, Communications in Nonlinear Science and Numerical Simulation, 15(11) (2010), 3547–3556.
  • [25] S. Zheng: Adaptive modified function projective synchronization of unknown chaotic systemswith different order. AppliedMathematics and Computation, 218(10) (2011), 5891–5899.
  • [26] L. Runzi, W. Yinglan, and D. Shucheng: Combination synchronization of three classic chaotic systems using active backstepping design. Chaos: An Interdisciplinary Journal of Nonlinear Science, 21(4) (2011), 043114, https://doi.org/10.1063/1.3655366.
  • [27] V. Yadav, G. Prasad, T. Som, and S. Das: Multi drive-one response synchronization for fractional-order chaotic systems. Nonlinear Dynamics, 70(2) (2012), 1263–1271.
  • [28] V. Yadav, G. Prasad, T. Som, and S. Das: Combined synchronization of time-delayed chaotic systems with uncertain parameters. Chinese Journal of Physics, 55(2) (2017), 457–466.
  • [29] C. Feng, Y. Tan, Y. Wang, and H. Yang: Active backstepping control of combined projective synchronization among different nonlinear systems. Automatika, 58(3) (2017), 295–301.
  • [30] S. F. Wang and D-Z Xu: The dynamic analysis of a chaotic system. Advances in Mechanical Engineering, 9(3) (2017), 1–6.
  • [31] Y. Xu, B. Li, Y. Wang, W. Zhou, and J.-A. Fang: A New Four-Scroll Chaotic Attractor Consisted of Two-Scroll TransientChaotic and Two-Scroll Ultimate Chaotic. Mathematical Problems in Engineering, 2012 (2012), Article ID 438328, 12 pages.
  • [32] C. Zhu, Y. Liu, and Y. Guo: Theoretic and Numerical Study of a New Chaotic System. Intelligent Information Management, 2 (2010), 104–109.
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-d54c58a9-f701-4451-9190-0f5381d42f87
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