A Research on the Synchronization of Two Novel Chaotic Systems Based on a Nonlinear Active Control Algorithm

  • I. Ahmad School of Quantitative Sciences, University Utara Malaysia, Alor Setar, Malaysia | College of Applied Sciences, Nizwa, Oman
  • A. Saaban School of Quantitative Sciences, University Utara Malaysia, Alor Setar, Malaysia
  • A. Ibrahin School of Quantitative Sciences, University Utara Malaysia, Alor Setar, Malaysia
  • M. Shahzad College of Applied Sciences, Nizwa, Oman
Keywords: Synchronization, Lyapunov Stability Theory, Nonlinear Control, Routh-Hurwitz Criterion


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.


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L. M. Pecora, T. L. Carroll, “Synchronization in chaotic systems”. Physical Review Letters, Vol. 64, No. 8, pp. 821–824, 1990

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

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

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

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

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

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

E. Lorenz, “Deterministic nonperiodic flow”, Journal of the Atmospheric Sciences, Vol. 20, No. 2, pp. 130–141, 1963

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

L. S. Tee, Z. Salleh, “Dynamical analysis of a modified Lorenz system”, Journal of Mathematics, Vol. 2013, Article ID 820946, 2013

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

G. Tigan, D. Opris, “Analysis of a 3D chaotic system”, Chaos, Solitons & Fractals, Vol. 36, No. 5, pp. 1315-1319, 2008

J. Lu. G. Chen, “A new chaotic attractor coined”, International Journal of Bifurcation and Chaos, Vol. 12, No. 3, pp. 659-662, 2002

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

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

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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