Abstract
In this paper, we investigate the transmission projective synchronization control problem for multiple, non-identical, coupled chaotic systems. By considering the influence of the occurrence of a fault between a driving system and a responding system, we define our new transmission synchronization scheme. After that, control laws are designed to achieve transmission projective synchronization and a simple stability criteria is obtained for reaching the transmission synchronization among multi-systems. A numerical example is used to verify the effectiveness of the synchronization within a desired scaling factor.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
References
Pecora, L.M., Carroll, T.L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64, 821–824 (1990)
Sun, J., Shen, Y., Zhang, G.D., et al.: Combination-combination synchronization among four identical or different chaotic systems. Nonlinear Dyn. 73, 1211–1222 (2013)
Jiang, C.M., Liu, S.T.: Generalized combination complex synchronization of new hyperchaotic complex Lü-like systems. Adv. Differ. Equ. 214, 1–17 (2015)
Chen, X.Y., Qiu, J.L., Cao, J.D., He, H.B.: Hybrid synchronization behavior in an array of coupled chaotic systems with ring connection. Neurocomputing 173, 1299–1309 (2016)
Bhowmick, S.K., Ghosh, D.: Targeting engineering synchronization in chaotic systems. Int. J. Mod. Phys. C 27, 1650006 (2016)
Sun, J., Shen, Y., Yin, Q., Xu, C.J.: Compound synchronization of four memristor chaotic oscillator systems and secure communication. Chaos 23, 013140 (2013)
Sun, J., Shen, Y., Zhang, G.D.: Transmission projective synchronization of multi-systems with non-delayed and delayed coupling via impulsive control. Chaos 22, 043107 (2012)
Chen, X.Y., Qiu, J.L., Song, Q., Zhang, A.C.: Synchronization of N coupled chaotic systems with ring connection based on special antisymmetric structure. Abstr. Appl. Anal. 2013, 680604 (2013)
Chen, X.Y., Wang, C.Y., Qiu, J.L.: Synchronization and anti-synchronization of N different coupled chaotic systems with ring connection. Int. J. Mod. Phys. C 25, 1–12 (2014)
Gong, H.C., Chen, X.Y., Qiu, J.L., et al.: Generalized projective synchronization of an array of non-identical coupled chaotic systems. In: The 26th Chinese Control and Decision Conference, pp. 119–123. IEEE Press, New York (2014)
Yu, Y., Zhang, S.: Global synchronization of three coupled chaotic systems with ring connection. Chaos Solitions Fractals 24, 1233–1242 (2005)
Liu, Y., Lü, L.: Synchronization of N different coupled chaotic systems with ring and chain connections. Appl. Math. Mech. 29, 1181–1190 (2008)
Tang, Y., Fang, J.A.: Synchronization of N-coupled Fractional-order chaotic systems with ring connection. Commun. Nonlinear Sci. Numer. Simul. 15, 401–412 (2010)
Yang, L., Zhang, J.: Synchronization of three identical systems and its application for secure communication with noise perturbation. In: International Conference on Information Engineering and Computer Science, pp. 1–4. IEEE Press, New York (2009)
Cheng, L.Y., Chen, X.Y., Qiu, J.L., et al.: Transmission projective synchronization in an array of identical coupled chaotic systems. In: The 33th Chinese Control Conference, pp. 2789–2793. IEEE Press, New York (2014)
Cai, N., Jing, Y.W., Zhang, S.Y.: Generalized projective synchronization of different chaotic systems based on antisymmetric structure. Chaos Solitons Fractals 42, 1190–1196 (2009)
Liu, B., Zhang, K.: Stability of nonlinear systems with tridiagonal structure and its applications. Acta Autom. Sin. 33, 442–446 (2007)
Acknowledgement
This work was supported in part by the Applied Mathematics Enhancement Program (AMEP) of Linyi University and the National Natural Science Foundation of China (No.61403179, 61273012), by a Project of the Postdoctoral Sustentation Fund of Jiangsu Province under Grant 1402042B.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Chen, X., Cao, J., Qiu, J., Yang, C. (2016). Transmission Synchronization Control of Multiple Non-identical Coupled Chaotic Systems. In: Cheng, L., Liu, Q., Ronzhin, A. (eds) Advances in Neural Networks – ISNN 2016. ISNN 2016. Lecture Notes in Computer Science(), vol 9719. Springer, Cham. https://doi.org/10.1007/978-3-319-40663-3_33
Download citation
DOI: https://doi.org/10.1007/978-3-319-40663-3_33
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-40662-6
Online ISBN: 978-3-319-40663-3
eBook Packages: Computer ScienceComputer Science (R0)