AM  Vol.6 No.11 , October 2015
Chaos Synchronization in Lorenz System
Author(s) Ayub Khan1, Prempal Singh2
ABSTRACT
In this paper, we analyze chaotic dynamics of nonlinear systems and study chaos synchronization of Lorenz system. We extend our study by discussing other methods available in literature. We propose a theorem followed by a lemma in general and another one for a particular case of Lorenz system. Numerical simulations are given to verify the proposed theorems.

Cite this paper
Khan, A. and Singh, P. (2015) Chaos Synchronization in Lorenz System. Applied Mathematics, 6, 1864-1872. doi: 10.4236/am.2015.611164.
References
[1]   Pecora, L.M. and Carroll, T.L. (1990) Synchronization of Chaotic Systems. Physical Review Letters, 64, 821-823.
http://dx.doi.org/10.1103/PhysRevLett.64.821

[2]   Khan, A. and Singh, P. (2008) Non-Linear Dynamical System and Chaos Synchronization. International Journal of Bifurcation and Chaos, 18, 1531-1537.
http://dx.doi.org/10.1142/S0218127408021142

[3]   Li, D., Lu, J.A. and Wu, X.Q. (2005) Linearly Coupled Synchronization of the Unified Chaotic Systems and the Lorenz Systems. Chaos Solitons Fractals, 23, 79-85.
http://dx.doi.org/10.1016/j.chaos.2004.03.027

[4]   Yu, Y. and Zhang, S. (2004) The Synchronization of Linearly Bidirectional Coupled Chaotic Systems. Chaos Solitons Fractals, 22, 189-197.
http://dx.doi.org/10.1016/j.chaos.2003.12.088

[5]   Jiang, G. and Tang, W.K.S. (2002) A Global Chaos Synchronization Criterion for Coupled Chaotic Systems via Unidirectional Linear Error Feedback Approach. International Journal of Bifurcation and Chaos, 12, 2239-2253.
http://dx.doi.org/10.1142/S0218127402005790

[6]   Toa, C. (2006) Dislocated Feedback Synchronization of Lorenz Chaotic System. Physics Letters A, 348, 201-209.
http://dx.doi.org/10.1016/j.physleta.2005.08.060

[7]   Wang, Y., Guan, Z.H. and Wang, G.H.O. (2003) Feedback and Adaptive Control for the Synchronization of Chen System via a Single Variable. Physics Letters A, 312, 34-40.
http://dx.doi.org/10.1016/S0375-9601(03)00573-5

[8]   Hang, X., Lu, J.A. and Wu, X.Q. (2004) Adaptive Feedback Synchronization of Lu System. Chaos Solitons Fractals, 22, 221-227.
http://dx.doi.org/10.1016/j.chaos.2003.12.103

[9]   Yassen, M.T. (2005) Feedback and Adaptive Synchronization of Chaotic Lu Systems. Chaos Solitons Fractals, 23, 1319-1325.
http://dx.doi.org/10.1016/S0960-0779(04)00383-2

[10]   Liao, X. and Yu, P. (2006) Chaos Control for the Family of Rossler Systems Using Feedback Controllers. Chaos, Solitons and Fractals, 29, 91-107.
http://dx.doi.org/10.1016/j.chaos.2004.12.046

[11]   Liao, T.L. and Huang, N.S. (1999) An Observer-Based Approach for Chaotic Synchronization with Applications to Secure Communications. IEEE Transactions on Circuits and Systems I, 46, 1144-1150.
http://dx.doi.org/10.1109/81.788817

[12]   Sun, J. and Zhang, Y. (2004) Impulsive Control and Synchronization of Chua’s Oscillators. Mathematics and Computers in Simulation, 66, 499-508.
http://dx.doi.org/10.1016/j.matcom.2004.03.004

[13]   Xiong, W., Xei, W. and Cao, J. (2006) Adaptive Exponential Synchronization of Delayed Chaotic Networks. Physica A, 370, 832-842.
http://dx.doi.org/10.1016/j.physa.2006.03.002

[14]   Gonzalo, J., Cicese, B.R., Chen, G. and Shieh, L.S. (2004) Fuzzy Chaos Synchronization via Sampled Driving Signals. International Journal of Bifurcation and Chaos, 14, 2721-2733.
http://dx.doi.org/10.1142/S0218127404010965

[15]   Chang, W.D. and Yan, J.J. (2005) Adaptive Robust PID Controller Design Based on Sliding Mode for Uncertain Chaotic Systems. Chaos, Solitons and Fractals, 26, 167-175.
http://dx.doi.org/10.1016/j.chaos.2004.12.013

[16]   Jang, M.J., Chen, C.C. and Chen, C.O. (2002) Sliding Mode Control of Chaos in the Cubic Chua’s Circuit System. International Journal of Bifurcation and Chaos, 12, 1437-1449.
http://dx.doi.org/10.1142/S0218127402005248

[17]   Liao, T.L., Yan, J.J. and Hou, Y.Y. (2008) Robust Chaos Suppression for the Family of Nonlinear Chaotic Systems with Noise Perturbation. Nonlinear Analysis, 69, 14-23.

[18]   di Bernardo, M. (1996) Adaptive Controller to Synchronize and Control Chaotic Systems. Physics Letters A, 214, 139-144.
http://dx.doi.org/10.1016/0375-9601(96)00182-X

[19]   Khadra, A. (2004) Impulsive Control and Synchronization of Chaos-Generating-Systems with Applications to Secure Communication. Master’s Thesis, University of Waterloo, Waterloo.

 
 
Top