Abstract and Applied Analysis
Volume 2014 (2014), Article ID 257327, 16 pages
http://dx.doi.org/10.1155/2014/257327
Research Article
A Novel Four-Wing Hyperchaotic Complex System and Its Complex Modified Hybrid Projective Synchronization with Different Dimensions
1School of Control Science and Engineering, Shandong University, Ji’nan 250061, China
2School of Mathematical Sciences, University of Ji’nan, Ji’nan 250022, China
Received 4 March 2014; Revised 12 May 2014; Accepted 16 May 2014; Published 5 June 2014
Academic Editor: Shurong Sun
Copyright © 2014 Jian Liu 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.
Linked References
- E. N. Lorenz, “Deterministic nonperiodic flow,” Journal of the Atmospheric Sciences, vol. 20, pp. 130–141, 1963. View at Google Scholar
- D. J. Tritton, Physical Fluid Dynamics, Clarendon Press, 1988. View at MathSciNet
- J. D. Gibbon and M. J. McGuinness, “The real and complex Lorenz equations in rotating fluids and lasers,” Physica D. Nonlinear Phenomena, vol. 5, no. 1, pp. 108–122, 1982. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- A. C. Fowler, M. J. McGuinness, and J. D. Gibbon, “The complex Lorenz equations,” Physica D. Nonlinear Phenomena, vol. 4, no. 2, pp. 139–163, 1981/82. View at Publisher · View at Google Scholar · View at MathSciNet
- A. Rauh, L. Hannibal, and N. B. Abraham, “Global stability properties of the complex Lorenz model,” Physica D. Nonlinear Phenomena, vol. 99, no. 1, pp. 45–58, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- G. M. Mahmoud, M. A. Al-Kashif, and S. A. Aly, “Basic properties and chaotic synchronization of complex Lorenz system,” International Journal of Modern Physics C, vol. 18, no. 2, pp. 253–265, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- A. H. Nayfeh and D. T. Mook, Nonlinear Oscillations, Wiley, New York, NY, USA, 1979. View at MathSciNet
- A. C. Newell and J. V. Moloney, Nonlinear Optics, Addison-Wesley, Reading, Mass, USA, 1992. View at MathSciNet
- V. A. Rozhanskii and L. D. Tsendin, Transport Phenomena in Partially Ionized Plasma, Taylor and Francis, London, UK, 2001.
- L. Cveticanin, “Resonant vibrations of nonlinear rotors,” Mechanism and Machine Theory, vol. 30, no. 4, pp. 581–588, 1995. View at Google Scholar
- R. Dilao and R. Alves-Pires, Nonlinear Dynamics in Particle Accelerators, World Scientific, Singapore, 1996.
- G. M. Mahmoud, “Approximate solutions of a class of complex nonlinear dynamical systems,” Physica A. Statistical Mechanics and Its Applications, vol. 253, no. 1, pp. 211–222, 1998. View at Google Scholar
- L. Cveticanin, “Analytic approach for the solution of the complex-valued strong non-linear differential equation of Duffing type,” Physica A. Statistical Mechanics and Its Applications, vol. 297, no. 3-4, pp. 348–360, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- G. M. Mahmoud, A. A. Mohamed, and S. A. Aly, “Strange attractors and chaos control in periodically forced complex Duffing's oscillators,” Physica A. Statistical Mechanics and Its Applications, vol. 292, no. 1–4, pp. 193–206, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- G. M. Mahmoud and T. Bountis, “The dynamics of systems of complex nonlinear oscillators: a review,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 14, no. 11, pp. 3821–3846, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- G. M. Mahmoud and E. E. Mahmoud, “Synchronization and control of hyperchaotic complex Lorenz system,” Mathematics and Computers in Simulation, vol. 80, no. 12, pp. 2286–2296, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- P. Liu and S. T. Liu, “Robust adaptive full state hybrid synchronization of chaotic complex systems with unknown parameters and external disturbances,” Nonlinear Dynamics, vol. 70, no. 1, pp. 585–599, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
- M. F. Hu, Z. Y. Xu, and R. Zhang, “Full state hybrid projective synchronization in continuous-time chaotic (hyperchaotic) systems,” Communications in Nonlinear Science and Numerical Simulation, vol. 13, no. 2, pp. 456–464, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- Y. Chu, Y. X. Chang, J. G. Zhang, X. F. Li, and X. L. An, “Full state hybrid projective synchronization in hyperchaotic systems,” Chaos, Solitons and Fractals, vol. 42, no. 3, pp. 1502–1510, 2009. View at Google Scholar
- F. F. Zhang and S. T. Liu, “Full state hybrid projective synchronization and parameters identification for uncertain chaotic (hyperchaotic) complex systems,” Journal of Computational and Nonlinear Dynamics, vol. 9, Article ID 021009, 2014. View at Google Scholar
- F. F. Zhang, S. T. Liu, and W. Y. Yu, “Modified projective synchronization with complex scaling factors of uncertain real chaos and complex chaos,” Chinese Physics B, vol. 22, Article ID 120505, 2013. View at Google Scholar
- G. M. Mahmoud and E. E. Mahmoud, “Complex modified projective synchronization of two chaotic complex nonlinear systems,” Nonlinear Dynamics, vol. 73, no. 4, pp. 2231–2240, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- Z. G. Li and D. L. Xu, “A secure communication scheme using projective chaos synchronization,” Chaos, Solitons and Fractals, vol. 22, no. 2, pp. 477–481, 2004. View at Google Scholar
- Z. Y. Wu, G. R. Chen, and X. C. Fu, “Synchronization of a network coupled with complex-variable chaotic systems,” Chaos, vol. 22, no. 2, Article ID 023127, 2012. View at Publisher · View at Google Scholar
- Y. Zhang and J. J. Jiang, “Nonlinear dynamic mechanism of vocal tremor from voice analysis and model simulations,” Journal of Sound and Vibration, vol. 316, no. 1–5, pp. 248–262, 2008. View at Publisher · View at Google Scholar
- 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. View at Google Scholar
- S. Dadras, H. R. Momeni, G. Qi, and Z.-l. Wang, “Four-wing hyperchaotic attractor generated from a new 4D system with one equilibrium and its fractional-order form,” Nonlinear Dynamics, vol. 67, no. 2, pp. 1161–1173, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- A. Wolf, J. B. Swift, H. L. Swinney, and J. A. Vastano, “Determining Lyapunov exponents from a time series,” Physica D. Nonlinear Phenomena, vol. 16, no. 3, pp. 285–317, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- H. C. Wei and X. C. Zheng, The Matrix Theory in Engineering, China University of Petroleum Press, Dongying, China, 1999.