Synchronization and Anti-Synchronization Of A Chaotic Satellite Under The Effect Of Magnetic Torque Via Active Control

0*, Mohammed Raziuddin**
* Department of General Requirements, College of Applied Sciences, Nizwa, Oman.
** Department of Information Technology, Nizwa College of Technology, Nizwa, Oman.
Periodicity:October - December'2013
DOI : https://doi.org/10.26634/jmat.2.4.2610

Abstract

The determination and prediction of the orbit of a satellite is influenced by the perturbing forces causing chaos. In this paper, we have discussed the synchronization and anti-synchronization (AS) behavior of two such identical planar oscillation of a satellite in elliptic orbit influenced by magnetic torque evolving from different initial conditions using the active control technique. The designed controllers, with our own choice of the coefficient matrix of the error dynamics are found to be effective to achieve synchronization and AS between the states variables of two chaotic identical dynamical systems under consideration. All the results are validated by numerical simulations using mathematica.

Keywords

Synchronization; Active Control; Lyapunov Stability; AS.

How to Cite this Article?

Mohammad Shahzad and Mohammad Raziuddin (2013). Synchronization and Anti-Synchronization of A Chaotic Satellite Under The Effect of Magnetic Torque via Active Control. i-manager’s Journal on Mathematics, 2(4), 7-13. https://doi.org/10.26634/jmat.2.4.2610

References

[1]. Pecora, L. M. & Carroll, T. L. (1990). Synchronization in chaotic systems. Physical Review Letters: 64, 821–824.
[2]. Lakshmanan, M & Murali, K. (1996). Chaos in Nonlinear Oscillators: Controlling and Synchronizing, World Scientific, Singapore.
[3]. Pikovsky, A., Rosenblum, M. & Kurths, J. (2001). Synchronization: A Unified Approach to Nonlinear Science, Cambridge University Press, Cambridge.
[4]. Ticos, C. M., Rosa Jr. E., Pardo, W. B., Walkenstein J. A. & Monti, M. (2000). Experimental real-time phase synchronization of paced chaotic plasma discharge, Physical Review Letters 85, 2929–2932.
[5]. Nimeijer, H. & Mareels Ivan, M. Y. (1997). An observer looks at synchronization, IEEE Transactions on Circuits and Systems I 44, 882–890.
[6]. Kim, C. M., Rim, S. Kye, W. H., Ryu, J. W. & Park, Y. J. (2000). Anti-synchronization of chaotic oscillators, Physics Letters A 320, 39–49.
[7]. Zhang Y. & Sun, J. (2004). Chaotic synchronization and anti-synchronization based on suitable separation, Physics Letters A 330, 442–447.
[8]. Emadzadeh, A. A. & Mohammed, H. (2005). Anti-synchronization of two different chaotic systems via active control, Transactions on Engineering, Computing and Technology 6, 62–65.
[9]. Li, C. & Liao, X. (2006). Anti-synchronization of a class of coupled chaotic systems via linear feedback control, International Journal of Bifurcation and Chaos 16, 1041–1047.
[10]. Nakata, S., Miyata, T., Ojima, N. & Yoshikawa, K. (1998). Self-synchronization in coupled salt–water oscillators, Physica D: 115, 313–320.
[11]. Idowu, B. A., Vincent. U. E. & Njah, A. N. (2007). Anti-synchronization of chaos in nonlinear gyros via active control, Journal of Mathematical Control Science and Applications 1,191–200.
[12]. Idowu, B. A., Vincent, U. E. & Obawole, A. O. (2007). Anti-synchronization between two new different chaotic systems via active control, Journal of the Nigerian Association of Mathematical Physics: 11, 15–20.
[13]. Vincent, U. E. & Ucar, A. (2007). Synchronization and anti-synchronization of chaos in permanent magnet reluctance machine, Far East Journal of Dynamical Systems: 9, 211–221.
[14]. Vincent, U. E. & Laoye, J. A. (2007). Synchronization, anti-synchronization and current transport in non-identical chaotic ratchets, Physica A 384, 230–240.
[15]. Bai, E. W., Lonngren, K. E. & Sprott, J. C. (2002). On the synchronization of a class of electronic circuits that exhibit chaos, Chaos, Solitons and Fractals 13, 1515–1521.
[16]. Chen, H. K. (2005). Synchronization of two different chaotic systems: a new system and each of the dynamical systems Lorenz, Chen and Lu, Chaos, Solitons and Fractals 25, 1049–1056.
[17]. Vincent, U. E. (2005). Synchronization of Rikitake chaotic attractor via active control, Physics Letters A: 343,133–138.
[18]. Vincent, U. E. (2008). Synchronization of identical and non-identical 4-D chaotic systems via active control, Chaos, Solitons and Fractals 37, 1065–1075.
[19]. Lei, Y., Xu, W. & Xie, W. (2007). Synchronization of two chaotic four-dimensional systems using active control, Chaos, Solitons and Fractals 32, 1823–1829.
[20]. Njah, A. N. & Vincent, U. E. (2008). Chaos synchronization between single and double wells Duffing Van-der Pol oscillators using active control, Chaos, Solitons and Fractals 37, 1356–1361.
[21]. Njah, A. N. (2006). Synchronization of forced damped pendulum via active control, Journal of the Nigerian Association of Mathematical Physics 10,143–148.
[22]. Ucar, A., Bai, E. W. & Lonngren, K. E. (2003). Synchronization of chaotic behavior in nonlinear Bloch equations, Physics Letters A 314, 96–101.
[23]. Lei, Y. , Xu, W. , Shen, J. & Fang, F. (2006). Global synchronization of two parametrically excited systems using active control, Chaos, Solitons and Fractals 28 ,428–436.
[24]. Ucar, A., Lonngren, K. E. & Bai, E. W. (2006). Synchronization of the unified chaotic systems via active control, Chaos, Solitons and Solitons 27, 1292–1297.
[25]. Ucar, A., Lonngren, K. E. & Bai, E. W. (2007). Chaos synchronization in RCL-shunted Josephson junction via active control, Chaos, Solitons and Fractals 31,105–111.
[26]. Vincent, U. E. & Laoye, J. A. (2007). Synchronization and control of directed transport in inertia ratchets via active control, Physics Letters A 363, 91–95.
[27]. Khan, A. & Shahzad, M. (2013). Synchronization of a circular restricted three body problem with Lorenz hyper chaotic system using robust adaptive sliding mode controller. Complexity, 18(6), 58-64.
[28]. Bhardwaj, R. & Kaur, P. (2006). Satellite's Motion Under the effect of magnetic Torque. American Journal of Applied Sciences: 3(6), 1899-1902.
[29]. Cai, G. & Zheng S. (2008). Anti-synchronization in different hyperchaotic systems, Journal of Information and Computing Science: 3,181-188.
[30]. Shahzad, M. (2011). Synchronization and anti-synchronization of planar oscillation of a satellite in an elliptic orbit via active control. Journal of Control Science & Engineering, article id: 816432.
[31]. Khan, A. & Shahzad, M. (2012). Computational study of synchronization & anti-synchronization in Mimas-Tethys system. i' manager's Journal on mathematics, 1(2), 26-33.
If you have access to this article please login to view the article or kindly login to purchase the article

Purchase Instant Access

Single Article

North Americas,UK,
Middle East,Europe
India Rest of world
USD EUR INR USD-ROW
Pdf 35 35 200 20
Online 35 35 200 15
Pdf & Online 35 35 400 25

Options for accessing this content:
  • If you would like institutional access to this content, please recommend the title to your librarian.
    Library Recommendation Form
  • If you already have i-manager's user account: Login above and proceed to purchase the article.
  • New Users: Please register, then proceed to purchase the article.