Open Access Open Access  Restricted Access Subscription or Fee Access

Global Chaos Synchronization of Liu-Su-Liu and Li Systems by Active Nonlinear Control

Dr. V. Sundarapandian

Abstract


This paper investigates the global chaos synchronization of identical Liu-Su-Liu systems (2006), identical Li systems (2009) and non-identical Liu-Su-Liu and Li chaotic systems. Active nonlinear control is the method adopted to achieve the complete synchronization of the identical and different Liu-Su-Liu and Li systems. Our stability results derived in this paper are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the nonlinear control method is effective and convenient to synchronize the identical and different Liu-Su-Liu and Li systems. Numerical simulations are shown to validate and illustrate the effectiveness of the synchronization results derived in this paper.

Keywords


Chaos Synchronization, Active Nonlinear Control, Chaos, Liu-Su-Liu System, Li System

Full Text:

PDF

References


K.T. Alligood, T. Sauer and J.A. Yorke, Chaos: An Introduction to Dynamical Systems, New York: Springer-Verlag, 1997.

H. Fujisaka and T. Yamada, “Stability theory of synchronized motion in coupled-oscillator systems,” Progress of Theoretical Physics, vol. 69, pp. 32-47, 1983.

L.M. Pecora and T.L. Carroll, “Synchronization in chaotic systems,” Physical Review Letters, vol. 64, pp. 821-824, 1990.

L.M. Pecora and T.L. Carroll, “Synchronizing in chaotic circuits,” IEEE Transactions on Circuits and Systems, vol. 38, pp. 453-456, 1991.

M. Lakshmanan and K. Murali, Chaos in Nonlinear Oscillators: Controlling and Synchronization, World Scientific, Singapore, 1996.

S.K. Han, C. Kerrer and Y. Kuramoto, “D-phasing and bursting in coupled neural oscillators,” Physical Review Letters, vol. 75, pp. 3190-3193, 1995.

B. Blasius, A. Huppert and L. Stone, “Complex dynamics and phase synchronization in spatially extended ecological system,” Nature, Vol. 399, pp. 354-359, 1999.

J. Lu, X. Wu, X. Han and J. Lü, “Adaptive feedback synchronization of a unified chaotic system,” Physics Letters A, vol. 329, pp. 327-333, 2004.

L. Kocarev and U. Partliz, “General approach for chaotic synchronization with applications to communications,” Physical Review Letters, vol. 74, pp. 5028-5030, 1995.

K. Murali and M. Lakshmanan, “Secure communication using a compound signal using sampled-data feedback,” Applied Mathematics and Mechanics, vol. 11, pp. 1309-1315, 2003.

T. Yang and L.O. Chua, “Generalized synchronization of chaos via linear transformation,” International Journal of Bifurcation and Chaos, vol. 9, pp. 215-219, 1999.

E. Ott, C. Grebogi and J.A. Yorke, “Controlling chaos,” Physical Review Letters, vol. 64, pp. 1196-1199, 1990.

J.H. Park and O.M. Kwon, “A novel criterion for delayed feedback control of time-delay chaotic systems,” Chaos, Solitons and Fractals, vol. 17, pp. 709-716, 2003.

X. Wu and J. Lü, “Parameter identification and backstepping control of uncertain Lü sysetm,” Chaos, Solitons and Fractals, vol. 18, pp. 721-729, 2003.

T.L. Liao and S.H. Tsai, “Adaptive synchronization of chaotic systems and its applications to secure communications”, Chaos, Solitons and Fractals, vol. 11, pp. 1387-1396, 2000.

Y.G. Yu and S.C. Zhang, “Adaptive backstepping synchronization of uncertain chaotic systems,” Chaos, Solitons and Fractals, vol. 27, pp. 1369-1375, 2006.

J.H. Park, S.M. Lee and O.M. Kwon, “Adaptive synchronization of Genesio-Tesi chaotic system via a novel feedback control,” Physics Letters A, vol. 371, pp. 263-270, 2007.

J.H. Park, “Adaptive control for modified projective synchronization of a four-dimensional chaotic system with uncertain parameters,” Journal of Computational and Applied Mathematics, vol. 213, pp. 288-293, 2008.

J.H. Park, “Chaos synchronization of nonlinear Bloch equations,” Chaos, Solitons and Fractals, vol. 27, pp. 357-361, 2006.

H.T. Yau, “Design of adaptive sliding mode controller for chaos synchronization with uncertaintities,” Chaos, Solitons and Fractals, vol. 22, pp. 341-347, 2004.

X. Zhang and H. Zhu, “Anti-synchronization of two different hyperchaotic systems with active and adaptive control,” International Journal of Nonlinear Science, vol. 6, pp. 216-223, 2008.

R. Vicente, J. Dauden, P. Colet and R. Toral, “Analysis and characterization of the hyperchaos generated by semiconductor laser object,” IEEE J. Quantm Electronics, vol. 41, pp. 541-548, 2005.

L. Liu, Y.C. Su and C.X. Liu, “A modified Lorenz system,” Internat. J. Nonlinear Science and Numerical Simulation, vol. 7, pp. 187-190, 2006.

X.F. Li, K.E. Chlouveakis and D.L. Xu, “Nonlinear dynamics and circuit relaization of a new chaotic flow: A variant of Lorenz, Chen and Lü,” Nonlinear Analysis, vol. 10, pp. 2357-2368, 2009.

W. Hahn, The Stability of Motion, Springer, Berlin, 1967.


Refbacks

  • There are currently no refbacks.


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.