Controlling Chaos in Damped and Driven Morse Oscillator via Slave-Master Feedback

• Authors: S. Behnia , A. Akhshani , M. Panahi , R. Asadi
• Languages of publication: EN

Abstracts

EN

The dynamical behavior of the Morse oscillator is investigated primarily by means of the Lyapunov exponent and bifurcation diagrams. Then, the problem of controlling chaos for this oscillator is studied using a new method introduced by Behnia and Akhshani, which is based on the construction of slave-master feedback. In the control model based on slave-master feedback, the oscillator as the slave system is coupled with a dynamical system as the master, so its implementation becomes quite simple and similar statements can be made for the high dimensional cases. The validity of this method is verified by numerical simulations. The obtained results show the effectiveness of the proposed control model.

Keywords

EN

05.45.-a; 05.45.Gg; 05.45.Pq

Discipline

• 05.45.-a: Nonlinear dynamics and chaos(see also section 45 Classical mechanics of discrete systems; for chaos in fluid dynamics, see 47.52.+j; for chaos in superconductivity, see 74.40.De)
• 05.45.Gg: Control of chaos, applications of chaos
• 05.45.Pq: Numerical simulations of chaotic systems

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2013
• Volume: 123
• Issue: 1
• Pages: 7-12

Dates

published

2013-01

received

2012-05-06

(unknown)

2012-05-17

Contributors

author

S. Behnia

• Department of Physics, Urmia University of Technology, Orumieh, Iran

author

A. Akhshani

• Department of Physics, IAU, Orumieh Branch, Orumieh, Iran
• School of Physics, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia

author

M. Panahi

• Department of Physics, IAU, Orumieh Branch, Orumieh, Iran

author

R. Asadi

• Department of Computer, IAU, Orumieh Branch, Orumieh, Iran

References

• [1] G. Dong, From Chaos to Order: Perspectives, Methodologies, Applications, World Sci., Singapore 1998
• [2] A. Saha, P. Wahi, J. Sound Vibrat. 330, 6070 (2011)
• [3] K. Ding, Q.L. Han, J. Sound Vibrat. 330, 2419 (2011)
• [4] Y.B. Peng, R. Ghanem, J. Li, J. Sound Vibrat. 329, 3660 (2010)
• [5] A.N. Njah, U.E. Vincent, J. Sound Vibrat. 319, 41 (2009)
• [6] S.Y. Liu, X. Yu, S.J. Zhu, J. Sound Vibrat. 310, 855 (2008)
• [7] X. Li, W. Xu, Y. Xiao, J. Sound Vibrat. 314, 526 (2008)
• [8] Z. Rahmani, M.R. Jahed Motlagh, Chaos Solitons Fractals 41, 1697 (2009)
• [9] H. Salarieh, A. Alasty, Chaos, Solitons, Fractals 41, 67 (2009)
• [10] T. Ueta, Int. J. Bifurcat. Chaos. 9, 1465 (1999)
• [11] T. Ueta, G. Chen, Int. J. Bifurcat. Chaos. 10, 1917 (2000)
• [12] E. Ott, C. Grebogi, J.A. Yorke, Phys. Rev. Lett. 64, 1196 (1990)
• [13] C.C. Fuh, P.C. Tung, Phys. Rev. Lett. 75, 2952 (1995)
• [14] G. Dong X, IEEE Trans. Circ. Syst. 40, 591 (1993)
• [15] M.T. Yassen, Chaos Solitons Fractals 15, 271 (2003)
• [16] M.T. Yassen, Chaos Solitons Fractals 26, 913 (2005)
• [17] H.N Agiza, Chaos Solitons Fractals 12, 341 (2002)
• [18] E.N. Sanchez, J.P. Perez, M. Martinez, G. Chen, Latin Am. Appl. Res: Int. J. 32, 111 (2002)
• [19] M.T. Yassen, Appl. Math. Comp. 135, 113 (2001)
• [20] T.-L. Liao, S-H. Lin, J. Frankl. Inst. 336, 925 (1999)
• [21] J. Lü, S. Zhang, Phys. Lett. A 286, 148 (2001)
• [22] J.M. Yuan, in: Directions in Chaos, Ed. B.L. Hao, World Sci., Singapore 1987, p. 164
• [23] R.B. Walker, R.K. Preston, J. Chem. Phys. 67, 2017 (1997)
• [24] S.K. Grap, J. Chem. Phys. 75, 67 (1983)
• [25] J.R. Ackerhalt, P.O.M. Milonni, Phys. Rev. A 34, 1211 (1986)
• [26] P.S. Dardi, S.K. Gray, J. Chem. Phys. 77, 1345 (1982)
• [27] F.W. Josellis, J. Differ. Equations 111, 360 (1994)
• [28] H. Kobessi, M. Kobessi, C.H. Tard, Can. J. Phys. 72, 80 (1994)
• [29] C.G. Lie, J.M. Yuan, J. Chem. Phys. 84, 5486 (1986)
• [30] D. Permann, I. Hamilton, J. Chem. Phys. 100, 379 (1994)
• [31] K.M. Christoffel, J.M. Bowman, J. Phys. Chem. 85, 2159 (1981)
• [32] R. Kapral, M. Schell, S. Fraser, J. Phys. Chem. 86, 2205 (1982)
• [33] Z. Jing, J. Deng, J. Yang, Chaos Solitons Fractals 35, 486 (2008)
• [34] S. Behnia, A. Akhshani, Chaos Solitons Fractals 42, 2105 (2009)
• [35] B.A. Pettitt, J. Chem. Educ. 75, 1170 (1998)
• [36] J. Wu, J. Cao, J. Chem. Phys. 115, 5381 (2001)
• [37] U. Leonhardt, Phys. Rev. A 55, 3164 (1997)
• [38] S. Krempl, T. Eisenhammer, A. Hübler, G. Mayer-Kress, Phys. Rev. Lett. 69, 430 (1992)
• [39] M.A. Jafarizadeh, S. Behnia, S. Khorram, H. Nagshara, J. Statist. Phys. 104, 1013 (2001)
• [40] S. Boccaletti, C. Grebogi, Y.-C. Lai, H. Mancini, D. Maza, Phys. Rep. 329, 103 (2000)
• [41] K. Umeno, Phys. Rev. E 55, 5280 (1997)
• [42] P.M. Morse, Phys. Rev. 34, 57 (1929)
• [43] M.E. Goggin, P.W. Milonni, Phys. Rev. A 37, 796 (1988)
• [44] S. Behnia, S. Afrang, A. Akhshani, Kh. Mabhouti, 10.1016/j.ijleo.2012.01.013. Opt. - Int. J. Light Electron Opt., in press

Identifiers

DOI

10.12693/APhysPolA.123.7