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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 953265, 14 pages
Combination-Combination Synchronization of Four Nonlinear Complex Chaotic Systems
1School of Information Science and Engineering, Yunnan University, Kunming 650091, China
2School of Mathematics and Computer Science, Yunnan University of Nationalities, Kunming 650031, China
3Bureau of Asset Management, Yunnan University, Kunming 650091, China
Received 13 August 2013; Revised 25 October 2013; Accepted 30 October 2013; Published 3 February 2014
Academic Editor: Narcisa C. Apreutesei
Copyright © 2014 Xiaobing Zhou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- A. C. Fowler, M. J. McGuinness, and J. D. Gibbon, “The complex Lorenz equations,” Physica D, vol. 4, no. 2, pp. 139–163, 1981/82.
- C. Z. Ning and H. Haken, “Detuned lasers and the complex Lorenz equations: subcritical and supercritical Hopf bifurcations,” Physical Review A, vol. 41, pp. 3826–3837, 1990.
- J. D. Gibbon and M. J. McGuinness, “The real and complex Lorenz equations in rotating fluids and lasers,” Physica D, vol. 5, no. 1, pp. 108–122, 1982.
- G. M. Mahmoud and A. A. M. Farghaly, “Chaos control of chaotic limit cycles of real and complex van der Pol oscillators,” Chaos, Solitons and Fractals, vol. 21, no. 4, pp. 915–924, 2004.
- G. M. Mahmoud, T. Bountis, and E. E. Mahmoud, “Active control and global synchronization of the complex Chen and Lü systems,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 17, no. 12, pp. 4295–4308, 2007.
- G. M. Mahmoud, T. Bountis, M. A. Al-Kashif, and S. A. Aly, “Dynamical properties and synchronization of complex non-linear equations for detuned lasers,” Dynamical Systems, vol. 24, no. 1, pp. 63–79, 2009.
- E. E. Mahmoud, “Dynamics and synchronization of new hyperchaotic complex Lorenz system,” Mathematical and Computer Modelling, vol. 55, no. 7-8, pp. 1951–1962, 2012.
- G. M. Mahmoud, M. E. Ahmed, and N. Sabor, “On autonomous and nonautonomous modified hyperchaotic complex Lü systems,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 21, no. 7, pp. 1913–1926, 2011.
- G. M. Mahmoud and M. E. Ahmed, “A hyperchaotic complex system generating two-, three-, and four-scroll attractors,” Journal of Vibration and Control, vol. 18, no. 6, pp. 841–849, 2012.
- L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems,” Physical Review Letters, vol. 64, no. 8, pp. 821–824, 1990.
- G. Chen and X. Dong, From Chaos to Order: Methodologies, Perspectives and Applications, vol. 24, World Scientific Publishing, Singapore, 1998.
- A. A. Koronovskii, O. I. Moskalenko, and A. E. Hramov, “On the use of chaotic synchronization for secure communication,” Physics-Uspekhi, vol. 52, pp. 1213–1238, 2009.
- B. S. Dmitriev, A. E. Hramov, A. A. Koronovskii, A. V. Starodubov, D. I. Trubetskov, and Y. D. Zharkov, “First experimental observation of generalized synchronization phenomena in microwave oscillators,” Physical Review Letters, vol. 102, Article ID 074101, 2009.
- M. Hu, Y. Yang, Z. Xu, and L. Guo, “Hybrid projective synchronization in a chaotic complex nonlinear system,” Mathematics and Computers in Simulation, vol. 79, no. 3, pp. 449–457, 2008.
- S. Liu and P. Liu, “Adaptive anti-synchronization of chaotic complex nonlinear systems with unknown parameters,” Nonlinear Analysis: Real World Applications, vol. 12, no. 6, pp. 3046–3055, 2011.
- E. E. Mahmoud, “Modified projective phase synchronization of chaotic complex nonlinear systems,” Mathematics and Computers in Simulation, vol. 89, pp. 69–85, 2013.
- G. M. Mahmoud, E. E. Mahmoud, and A. A. Arafa, “On projective synchronization of hyperchaotic complex nonlinear systems based on passive theory for secure communications,” Physica Scripta, vol. 87, no. 5, Article ID 055002, 2013.
- X. B. Zhou, M. R. Jiang, and X. M. Cai, “Synchronization of a novel hyperchaotic complex-variable system based on finite-time stability Theory,” Entropy, vol. 15, pp. 4334–4344, 2013.
- R. Z. Luo, Y. L. Wang, and S. C. Deng, “Combination synchronization of three classic chaotic systems using active backstepping design,” Chaos, vol. 21, no. 4, Article ID 043114, 2011.
- X. B. Zhou, M. R. Jiang, and Y. Q. Huang, “Combination synchronization of three identical or different nonlinear complex hyperchaotic systems,” Entropy, vol. 15, pp. 3746–3761, 2013.
- J. Sun, Y. Shen, G. Zhang, C. Xu, and G. Cui, “Combination-combination synchronization among four identical or different chaotic systems,” Nonlinear Dynamics, vol. 73, no. 3, pp. 1211–1222, 2013.
- G. M. Mahmoud, M. A. Al-Kashif, and A. A. Farghaly, “Chaotic and hyperchaotic attractors of a complex nonlinear system,” Journal of Physics A, vol. 41, no. 5, Article ID 055104, 12 pages, 2008.
- G. M. Mahmoud, S. A. Aly, and M. A. AL-Kashif, “Dynamical properties and chaos synchronization of a new chaotic complex nonlinear system,” Nonlinear Dynamics, vol. 51, no. 1-2, pp. 171–181, 2008.
- R. Z. Luo and Y. L. Wang, “Finite-time stochastic combination synchronization of three different chaotic systems and its application in secure communication,” Chaos, vol. 22, no. 2, Article ID 023109, 2012.
- H. P. Ren, M. S. Baptista, and C. Grebogi, “Wireless communication with chaos,” Physical Review Letters, vol. 110, no. 18, Article ID 184101, 5 pages, 2013.