A Research on the Synchronization of Two Novel Chaotic Systems Based on a Nonlinear Active Control Algorithm
The problem of chaos synchronization is to design a coupling between two chaotic systems (master-slave/drive-response systems configuration) such that the chaotic time evaluation becomes ideal and the output of the slave (response) system asymptotically follows the output of the master (drive) system. This paper has addressed the chaos synchronization problem of two chaotic systems using the Nonlinear Control Techniques, based on Lyapunov stability theory. It has been shown that the proposed schemes have outstanding transient performances and that analytically as well as graphically, synchronization is asymptotically globally stable. Suitable feedback controllers are designed to stabilize the closed-loop system at the origin. All simulation results are carried out to corroborate the effectiveness of the proposed methodologies by using Mathematica 9.
Keywords:Synchronization, Lyapunov Stability Theory, Nonlinear Control, Routh-Hurwitz Criterion
L. M. Pecora, T. L. Carroll, “Synchronization in chaotic systems”. Physical Review Letters, Vol. 64, No. 8, pp. 821–824, 1990 DOI: https://doi.org/10.1103/PhysRevLett.64.821
M. Shahzad, I. Ahmad, “Experimental study of synchronization & Anti-synchronization for spin orbit problem of Enceladus”, International Journal of Control Science and Engineering, Vol. 3, No. 2, pp. 41-47, 2013
X. F. Wang, Z. Q. Wang, “Synchronization of Chua's oscillators with the third state as the driving signal”, International Journal of Bifurcation and Chaos, Vol. 8, No. 7, pp. 1599-1603, 1998 DOI: https://doi.org/10.1142/S021812749800125X
K. Miyakawa, T. Okabe, M. Mizoguchi, F. Sakamoto, “Synchronization in the discrete chemical oscillation system”, The Journal of Chemical Physics, Vol. 103, No. 22, pp. 9621-9625, 1995 DOI: https://doi.org/10.1063/1.469977
A. N. Pisarchik, F. T. Arecchi, R. Meucci, A. DiGarbo, “Synchronization of Shilnikov chaos in a CO2 laser with feedback”, Laser Physics, Vol. 11, No. 11, pp. 1235–1239, 2001
O. Moskalenko, A. A. Koronovskii, A. E. Hramov, “Generalized synchronization of chaos for secure communication: remarkable stability to noise”, Physics Letters A, Vol. 374, No. 29, pp. 2925-2931, 2010 DOI: https://doi.org/10.1016/j.physleta.2010.05.024
A. Saaban, A. Ibrahim, M. Shahzad, I. Ahmad, “Global chaos synchronization of identical and nonidentical chaotic systems using only two nonlinear controllers”, International Journal of Mathematical, Computational, Physical and Quantum Engineering, Vo. 7, No. 12, pp. 1182-1188, 2013
I. Ahmad, A. Saaban, A. Ibrahim, M. Shahzad, “Global chaos identical and nonidentical synchronization of a new 3-D chaotic system using linear active control”, Asia Journal of Applied Sciences, Vol. 2, No. 1, pp. 1-12, 2014
H. K. Chen, “Global chaos synchronization of new chaotic systems via nonlinear control”, Chaos, Solitons & Fractals, Vol. 23, No. 4, pp. 1245-1251, 2005 DOI: https://doi.org/10.1016/S0960-0779(04)00373-X
F. Yu, C. Wang, Y. Hu, J. Yin, “Projective synchronization of a five-term hyperbolic-type chaotic system with fully uncertain parameters”, Acta Physica Sinica, Vol. 61, No. 6, pp. 0605051-0605059, 2012
F. Yu, Y. Song, “Complete switched generalized function projective synchronization of a class of hyperchaotic systems with unknown parameters and disturbance inputs”, Journal of Dynamic Systems,
Measurement, and Control, Vol. 136, No. 1, pp. 0145051-0145056, 2014.
A. Saaban, A. Ibrahim, M. Shahzad, I. Ahmad, “Identical synchronization of a new chaotic system via nonlinear control and linear active control techniques: a comparative analysis”, International Journal of Hybrid Information Technology Vol.7, No.1, pp. 211-224, 2014 DOI: https://doi.org/10.14257/ijhit.2014.7.1.17
I. Ahmad, A. Saaban, A. Ibrahim, M. Shahzad, “Global chaos synchronization of two different chaotic systems using nonlinear control”, International Journal of Sciences: Basic and Applied Research, Vol. 14, No. 1, pp. 225-238, 2014 DOI: https://doi.org/10.1002/cplx.21573
E. Lorenz, “Deterministic nonperiodic flow”, Journal of the Atmospheric Sciences, Vol. 20, No. 2, pp. 130–141, 1963 DOI: https://doi.org/10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2
S. Boccaletti, C. Grebogi, Y. C. Lai, H. Mancini, D. Maza, “The control of chaos: theory and applications”, Physics Reports, Vol. 329, No. 3, pp.103-109, 2000 DOI: https://doi.org/10.1016/S0370-1573(99)00096-4
L. S. Tee, Z. Salleh, “Dynamical analysis of a modified Lorenz system”, Journal of Mathematics, Vol. 2013, Article ID 820946, 2013 DOI: https://doi.org/10.1155/2013/820946
G. Qi, G. Chen, A. A. van Wyk, B. J. van Wyk, Y. Zhang, “A four-wing chaotic attractor generated from a new 3-D quadratic autonomous system”, Chaos, Solitons & Fractals, Vol. 38, No. 3, pp. 705-721, 2008 DOI: https://doi.org/10.1016/j.chaos.2007.01.029
G. Tigan, D. Opris, “Analysis of a 3D chaotic system”, Chaos, Solitons & Fractals, Vol. 36, No. 5, pp. 1315-1319, 2008 DOI: https://doi.org/10.1016/j.chaos.2006.07.052
J. Lu. G. Chen, “A new chaotic attractor coined”, International Journal of Bifurcation and Chaos, Vol. 12, No. 3, pp. 659-662, 2002 DOI: https://doi.org/10.1142/S0218127402004620
F. Yu, C. Wang, “A novel three dimensional autonomous chaotic system with a quadratic exponential nonlinear term”, Engineering, Technology & Applied Science Research, Vol. 2, No. 2, pp. 209-215, 2012 DOI: https://doi.org/10.48084/etasr.86
C. Li, L. Wu, H. Li, Y. Tong, “A novel chaotic system and its topological horseshoe”, Nonlinear Analysis: Modelling and Control, Vol. 18, No. 1, pp. 66–77, 2013 DOI: https://doi.org/10.15388/NA.18.1.14032
H. K. Khalil, Non Linear dynamical Systems. Prentice Hall, 3rd edi, NJ, 07458, USA, 2002
R. C. Dorf, R. H. Bishop, Modern Control Systems, 9th Ed. Princeton Hall, USA, 2001
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