Abstract
In this paper a novel three dimensions chaotic system with uncertain parameters and lorenz hyperchaotic system are as examples, the function projective synchronization and parameters identification of different hyperchaotic systems are researched. First, based on the Lyapunov theory of stability and adaptive control method, the adaptive nonlinear controller and adaptive identifying rule to uncertain parameter are designed logically. And by the controller and identifying rule, the function projective synchronization of different systems between three dimensions response system with uncertain parameter and drive system is realized. Second, the feasibility of the controller and identifying rule to uncertain parameter designed in this paper is analyzed theoretically, and the function projective synchronization and parameters identification are proved strictly theoretically. Finally, the theoretical results are verified by numerical simulation.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Wang, G.R., Yu, X.L., Chen, S.G.: Chaotic control, synchronization and utilizing. National Defence Industry Press, Beijing (2001) (in Chinese)
Feng, C.W., Cai, L., Kang, Q., Zhang, L.S.: A novel three dimension autonomous chaotic system. Acta Phys. Sin. 60(3), 030503–030507 (2011) (in Chinese)
Pecora, L.M., Carroll, T.L.: Synchronization of chaotic systems. Physical Review Letters 64(8), 821–830 (1990)
Carroll, T.L., Pecora, L.M.: Synchronizing chaotic circuits. IEEE Transactions on Circuits and Systems 38(4), 453–456 (1991)
Dong, J., Zhang, G.J., Yao, H., et al.: The control of complete synchronization and anti-phase synchronization for hyperchaotic systems of different structures. Journal of Air Force Engineering University 13(5), 90–94 (2012)
Min, F.H., Wang, Z.Q.: General chaotic synchronization of identical and different novel hyperchaotic system. Journal of Electronics & Information Technology 30(12), 3031–3034 (2008) (in Chinese)
Zhang, G., Zhang, W.: Pulse synchronization of complex network. Journal of Dynamics and Control 7(1), 001–004 (2009)
Lu, J., Zhang, R., Xu, Z.Y.: Phase synchronization between two adjacent nodes in amplitude coupled dynamical networks. Acta Phys. Sin. 59(9), 5949–5953 (2010) (in Chinese)
Cai, N., Jing, Y.W., Zhang, S.Y.: Adaptive synchronization and anti-synchronization of two different chaotic systems. Acta Phys.Sin. 58(2), 0802–0813 (2009) (in Chinese)
Mainieri, R., Rehacek, J.: Projective synchronization in three-dimensional chaotic systems. Phys. Rev. Lett. 82(15), 3042–3045 (1999)
Li, Z.G., Xu, D.: Chaos. Solitons and Fractals 22, 477 (2004)
Chee, C.Y., Xu, D.: Chaos. Solitons and Fractals 23, 1063 (2005)
Kadir, A., Wang, X.Y., Zhao, Y.Z.: Projective synchronization for unified hyperchaotic systems. Acta Phys. Sin. 60(4), 040506 (2011) (in Chinese)
Cai, G.L., Tan, Z.M., Zhou, W.H., Tu, W.T.: Dynamical analysis of a new chaotic system and its chaotic control. Acta Phys. Sin. 56(11), 6230–6237 (2010) (in Chinese)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dong, J., Zhang, Gj., Yao, H., Wang, Xb., Wang, J. (2012). Function Projective Synchronization and Parameters Identification of Different Hyperchaotic Systems Based on Adaptive Control. In: Lei, J., Wang, F.L., Deng, H., Miao, D. (eds) Artificial Intelligence and Computational Intelligence. AICI 2012. Lecture Notes in Computer Science(), vol 7530. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33478-8_41
Download citation
DOI: https://doi.org/10.1007/978-3-642-33478-8_41
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33477-1
Online ISBN: 978-3-642-33478-8
eBook Packages: Computer ScienceComputer Science (R0)