Reduced Order Synchronization: A Comparison of Simulation between Mathematica & Matlab

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Nizwa College of Applied Sciences, University of Technology and Applied Sciences, Oman.
Periodicity:October - December'2019
DOI : https://doi.org/10.26634/jmat.8.4.17548

Abstract

The present study deals with the synchronization of chaotic systems of different orders. The author investigates the reduced-order synchronization (ROS) problem for a circular restricted three body problem (CRTBP)-Lorenz chaotic systems that are of different orders. The study of ROS has been carried out via a robust generalized active control technique together with the effect of both unknown model uncertainties and external disturbances. Also for the chosen master-slave combination, a comparison of computational study between Mathematica and Matlab has been presented in order to observe the variations. Furthermore, it is discussed that ROS is a special case for multi-switching synchronization of different orders of chaotic systems.

Keywords

Reduced-Order Synchronization, Mathematica, Matlab.

How to Cite this Article?

Shahzad, M. (2019). Reduced Order Synchronization: A Comparison of Simulation between Mathematica & Matlab. i-manager's Journal on Mathematics, 8(4), 1-9. https://doi.org/10.26634/jmat.8.4.17548

References

[1]. Aghababa, M. P., & Aghababa, H. P. (2012). Synchronization of nonlinear chaotic electromechanical gyrostat systems with uncertainties. Nonlinear Dynamics, 67(4), 2689-2701. https://doi.org/10.1007/s11071-011-0181-5
[2]. Ahmad, I., Saaban, A. B., Ibrahim, A. B., & Shahzad, M. (2015). Global chaos synchronization of new chaotic system using linear active control. Complexity, 21(1), 379-386. https://doi.org/10.1002/cplx.21573
[3]. Ahmad, I., Saaban, A. B., Ibrahim, A. B., Shahzad, M., & Naveed, N. (2016). The synchronization of chaotic systems with different dimensions by a robust generalized active control. Optik, 127(11), 4859-4871. https://doi.org/10.1016/j.ijleo.2015. 12.134
[4]. Al-sawalha, M. M., & Noorani, M. S. M. (2011). Adaptive increasing-order synchronization and anti-synchronization of chaotic systems with uncertain parameters. Chinese Physics Letters, 28(11), 1-3. https://doi.org/10.1088/0256-307X/28/11/ 110507
[5]. Castro-Ramírez, J., Martínez-Guerra, R., & Cruz-Victoria, J. C. (2015). A new reduced-order observer for the synchronization of nonlinear chaotic systems: an application to secure communications. Chaos: An Interdisciplinary Journal of Nonlinear Science, 25(10), 1-7. https://doi.org/10.1063/1.4934650
[6]. Femat, R., & Solís-Perales, G. (2002). Synchronization of chaotic systems with different order. Physical Review E, 65(3), 036226.
[7]. Ho, M. C., Hung, Y. C., Liu, Z. Y., & Jiang, I. M. (2006). Reduced-order synchronization of chaotic systems with parameters unknown. Physics Letters A, 348(3-6), 251-259. https://doi.org/10.1016/j.physleta.2005.08.076
[8]. Lorenz, E. N. (1963). Deterministic nonperiodic flow. Journal of the Atmospheric Sciences, 20(2), 130-141. https://doi. org/10.1175/1520-0469(1963)020%3C0130:DNF%3E2.0.CO;2
[9]. Njah, A. N. (2011). Synchronization via active control of parametrically and externally excited Φ6 Van der Pol and Duffing oscillators and application to secure communications. Journal of Vibration and Control, 17(4), 493-504. https://doi.org/ 10.1177%2F1077546309357024
[10]. Njah, A. N., & Vincent, U. E. (2009). Synchronization and anti-synchronization of chaos in an extended Bonhöffer–van der Pol oscillator using active control. Journal of Sound and Vibration, 319(1-2), 41-49. https://doi.org/10.1016/j.jsv.2008.05. 036
[11]. Ojo, K. S., Njah, A. N., Olusola, O. I., & Omeike, M. O. (2014). Generalized reduced-order hybrid combination synchronization of three Josephson junctions via backstepping technique. Nonlinear Dynamics, 77(3), 583-595.
[12]. Shahzad, M. (2015). The improved results with Mathematica and effects of external uncertainty and disturbances on synchronization using a robust adaptive sliding mode controller: a comparative study. Nonlinear Dynamics, 79(3), 2037- 2054. https://doi.org/10.1007/s11071-014-1793-3
[13]. Shahzad, M., & Ahmad, I. (2013). Experimental study of synchronization & Anti-synchronization for spin orbit problem of Enceladus. International Journal of Control Science and Engineering, 3(2), 41-47. https://doi.org/10.5923/j.control. 20130302.02
[14]. Shahzad, M., Ahmad, I., Saaban, A. B., & Ibrahim, A. B. (2016). Improved time response of stabilization in synchronization of chaotic oscillators using Mathematica. Systems, 4(2), 1-21. https://doi.org/10.3390/systems4020025
[15]. Sparrow, C. (1982). The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors. Springer.
[16]. Strogatz, S. H. (2011). Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering. Colorado, United States: Westview Press.
[17]. Szebehely, V. (1967). Theory of Orbits. New York: Academic Press.
[18]. Vincent, U. E., & Ucar, A. (2007). Synchronization and anti-synchronization of chaos in permanent magnet reluctance machine. Far East Journal of Dynamical System, 9, 211–221.
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