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Pabasteh, Marzieh, Naderi, Bashir, Zarei, Hasan. (1402). Synchronization a chaotic system with Quadratic terms using the contraction Method. سامانه مدیریت نشریات علمی, 12(2), 361-373. doi: 10.22034/cmde.2023.55987.2337
Marzieh Pabasteh; Bashir Naderi; Hasan Zarei. "Synchronization a chaotic system with Quadratic terms using the contraction Method". سامانه مدیریت نشریات علمی, 12, 2, 1402, 361-373. doi: 10.22034/cmde.2023.55987.2337
Pabasteh, Marzieh, Naderi, Bashir, Zarei, Hasan. (1402). 'Synchronization a chaotic system with Quadratic terms using the contraction Method', سامانه مدیریت نشریات علمی, 12(2), pp. 361-373. doi: 10.22034/cmde.2023.55987.2337
Pabasteh, Marzieh, Naderi, Bashir, Zarei, Hasan. Synchronization a chaotic system with Quadratic terms using the contraction Method. سامانه مدیریت نشریات علمی, 1402; 12(2): 361-373. doi: 10.22034/cmde.2023.55987.2337

Synchronization a chaotic system with Quadratic terms using the contraction Method

Computational Methods for Differential Equations
مقاله 12، دوره 12، شماره 2، خرداد 2024، صفحه 361-373    اصل مقاله (1.1 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2023.55987.2337
نویسندگان
Marzieh Pabasteh1؛ Bashir Naderi* 1؛ Hasan Zarei2
1Department of Mathematics, Payame Noor University, Tehran, Iran.
2Department of Mathematics, Payame Noor University, Tehran, Iran
چکیده
In this article, Synchronization and control methods are discussed as essential topics in science. The contraction method is an exciting method that has been studied for the synchronization of chaotic systems with known and unknown parameters. The controller and the dynamic parameter estimation are obtained using the contraction theory to prove the stability of the synchronization error and the low parameter estimation. The control scheme does not employ the Lyapunov method. For demonstrate the ability of the proposed method, we performed a numerical simulation and compared the result with the previous literature.
کلیدواژه‌ها
Contraction theory؛ Chaos؛ Synchronization
مراجع
  • [1] A. Allahem, Synchronized chaos of a three-dimensional system with quadratic terms. Mathematical Problems in Engineering J, (2020), 1–4.
  • [2] G. Baghdadi, S. Jafari, J. Sprott, F. Towhidkhah, and M. H. Golpayegani, A chaotic model of sustaining attention problem in attention deficit disorder, Comm. in Non. Sci. and Num. Sim, 20(1) (2015), 174–185.
  • [3] V. V. Buyadzhi, A. V. Glushkov, O. Y. Khetselius, A. A. Kuznetsova, A. A. Buyadzhi, G. P. Prepelitsa, and V. B. Ternovsky, Nonlinear dynamics of laser systems with elements of a chaos: Advanced computational code, In Journal of Physics: Conference Series (Vol. 905, No. 1, p. 012007). IOP Publishing, (2017).
  • [4] Y. Chang, X. Wang, and D. Xu, Bifurcation analysis of a power system model with three machines and four buses, Bifurcation and Chaos J, 26(05) (2016), 1650082.
  • [5] S. L. De Souza and I. L. Caldas,Calculation of Lyapunov exponents in systems with impacts, Chaos, Solitons and Fractals J, 19(3) (2004), 569–579.
  • [6] X. Ge, B. Lu, F. Liu, and X. Luo, cryptanalyzing an image encryption algorithm with compound chaotic stream cipher based on perturbation, Nonlinear Dynamics J, 90 (2017), 1141–1150.
  • [7] M. Krstic, P. V. Kokotovic, and I. Kanellakopoulos, Nonlinear and adaptive control design, John Wiley and Sons, Inc, 1995.
  • [8] Y. Liu and X. Tong, Hyperchaotic system-based pseudorandom number generator, IET Information Security J, 10(6) (2016), 433–441.
  • [9] W. Lohmiller and J. J. E. Slotine, On contraction analysis for Nonlinear systems, Automatica J, 34(6) (1998), 683–696.
  • [10] W. Lohmiller, Contraction analysis of Nonlinear systems, Department of Mechanical Engineering, MIT, 1999. Thesis (Ph.D.).
  • [11] W. Lohmiller and J. J. E Slotine, Control system design for mechanical systems using Contraction theory, IEEE Transactions on Automatic Control J, 45(5) (2000), 984–989.
  • [12] X. Liu, L. Chen, Y. Zhao, and X. Song, Dynamic Stability of a class of fractional-order Nonlinear systems via fixed point theory, Math Meth Appl Sci J, 45 (2022), 77–92.
  • [13] Y. Long, S. Liu, L. Xie, and K. H. Johansson, Distributed Nonlinear model predictive control based on contraction theory, Robust Nonlinear Control J, (2017), 1–12.
  • [14] E. N. Lorenz, The mechanics of vacillation, Atmospheric Sciences J, 20(5) (1963), 448–465.
  • [15] S. Lynch, Dynamical Systems with Applications using MATLAB, Birkh¨auser J, 2004.
  • [16] Y. Ma, J. Mou, S. Banerjee, and M. Miao, A quartic nonlinear flux-controlled memristor model and its application in chaotic system, Applied and Computational Mathematics J, 22(3) (2023), 317–337.
  • [17] S. Mohammadi and R. Hejazi, Optimal fractional order PID controller performance in chaotic system of HIV disease: particle swarm and genetic algorithms optimization method. Computational Methods for Differential Equations J, 11(2) (2023), 207–224.
  • [18] G. Molnar, W. Taylor, and A. Langworthy, Mayo Clinic Proceedings, 47(10), 709 (1972).
  • [19] B. Naderi and H. Kheiri, Exponential synchronization of chaotic system and application in secure communication, Optik J, 127(5) (2016), 2407–2412.
  • [20] B. Naderi, H. Kheiri, and A.Heydari, Secure communication based on synchronization of three chaotic systems, Nonlinear Science J, 27(1) (2019), 53–64.
  • [21] R. Ofir, M. Margaliot, and Y. Levron, A sufficient condition for k-contraction of the series connection of two systems, IEEE Transactions on Automatic Control J, (2022).
  • [22] L. M. Pecora and T. L. Carroll, synchronization in chaotic systems, Physical Review Letters J, 64(8) (1990), 821.
  • [23] Y. Scharf, A chaotic outlook on biological systems, Chaos, Solitons and Fractals J, 95 (2017), 42–47.
  • [24] B. B. Sharma and I. N. Kar, Contraction theory-based recursive design of stabilizing controller for a class of Nonlinear systems, IET control theory and applications J, 4(6) (2010), 1005–1018.
  • [25] B. B. Sharma and I. N. Kar, Contraction theory based adaptive synchronization of chaotic systems, Chaos, Solitons and Fractals J, 41(5)(2009), 2437–2447.
  • [26] B. B. Sharma and I.N. Kar, Observer-based synchronization scheme for a class of chaotic systems using contraction theory, Nonlinear Dynamics J, 63(3) (2011), 429–445.
  • [27] J. P. Singh and B. K. Roy, Hidden attractors in a new complex generalized Lorenz hyperchaotic system, its synchronization using adaptive contraction theory, circuit validation , and application, Nonlinear Dynamics J, 92 (2018), 373–394.
  • [28] J. P. Singh, S. Jafari, A. J. M. Khalaf, V. T. Pham, and B. K. Roy, A modified chaotic oscillator with megastability and variable boosting and its synchronization using contraction theory-based control which is better than backstepping and Nonlinear active control, Pramana J, 94 (2020), 1–14.
  • [29] R. Soltani, B. Naderi, S. Nezhadhossein, and A. Heydari, Synchronization Control Strategy of Inverted Pendulums using Control Law Partitioning and Contraction Theory, Industrial Electronics Control and Optimization J, 6(2) (2023), 113–122.
  • [30] S. Strogatz, Nonlinear Dynamics and Chaos, Addison Wesley, Reading, MA J, (1994).
  • [31] P. Trikha, L. S. Jahanzaib, and T. Khan, Synchronization between integer and fractional chaotic systems Via tracking control and non linear control with application. Computational Methods for Differential Equations J, 10(1) (2022), 109–120.
  • [32] M. T. Yassen, Controlling chaos and synchronization for the new chaotic system using linear feedback control. Chaos, Solitons and Fractals J, 26(3) (2005), 913–920.
  • [33] X. Zhang and B. Cui, Synchronization of Lurie system based on contraction analysis, Applied Mathematics and Computation J, 223 (2013), 180–190.
  • [34] Z. Zhang, G. Chen, and S. Yu, Hyperchaotic signal generation via DSP for efficient perturbations to liquid mixing, Circuit Theory and Applications J, 37(1) (2009), 31–41.
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