Abstract
The issue of impulsive synchronization of the coupled Newton–Leipnik system is investigated. Based on the impulsive stability theory, nonlinear observer-based impulsive synchronization scheme is derived. A new and less conservative criteria for impulsive synchronization via nonlinear observer is proposed. The boundary of the stable regions is also estimated. One important advantage of the proposed method is that it is also applicable for the systems with more than one attractor. Numerical simulations on Newton–Leipnik system are illustrated to verify the theoretical results.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
Fujisaka, H., Yamada, T.: Stability theory of synchronized motion in coupled-oscillator systems. Prog. Theor. Phys. 69, 32–47 (1983)
Pecora, L.M., Carroll, T.L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64, 821–824 (1990)
Rosenblum, M., Pikovsky, A., Kurths, J.: Phase synchronization of chaotic oscillators. Phys. Rev. Lett. 76, 1804–1807 (1996)
Boccaletti, S., Pecora, L.M., Pelaez, A.: Unifying framework for synchronization of coupled dynamical systems. Phys. Rev. E 63, 066219 (2001)
Carroll, T.L., Pecora, L.M.: Synchronizing chaotic circuits. IEEE Trans. Circuits Syst. 38, 453–456 (1991)
Banerjee, S., Ghosh, D., Roy Chowdhury, A.: Multiplexing synchronization and its applications in cryptography. Phys. Scr. 78, 015010 (2008)
Banerjee, S., Ghosh, D., Ray, A., Roy Chowdhury, A.: Synchronization between two different time delayed systems and image encryption. Europhys. Lett. 81, 20006 (2008)
Ghosh, D., Banerjee, S., Roy Chowdhury, A.: Synchronization between variable time delayed systems and cryptography. Europhys. Lett. 80, 30006 (2007)
Ghosh, D.: Nonlinear active observer-based generalized synchronization in time-delayed systems. Nonlinear Dyn. doi:10.1007/s11071-009-9538-4. (Published online: 10 June, 2009)
Ghosh, D.: Nonlinear observer-based synchronization scheme for multiparameter estimation. Europhys. Lett. 84, 40012 (2008)
Ghosh, D., Banerjee, S.: Adaptive scheme for synchronization-based multiparameter estimation from a single chaotic time series and its applications. Phys. Rev. E 78, 056211 (2008)
Lakshmikantham, V., Bainov, D., Simeonov, P.: Theory of Impulsive Differential Equations. World Scientific, Singapore (1989)
Sun, J., Zhang, Y.: Impulsive control of Rössler systems. Phys. Lett. A 306, 306–312 (2003)
Yang, T., Yang, L.B., Yang, C.M.: Impulsive synchronization of Lorenz systems. Phys. Lett. A 226, 349–354 (1997)
Itoh, M., Yang, T., Chua, L.O.: Conditions for impulsive synchronization of chaotic and hyperchaotic systems. Int. J. Bifurc. Chaos 11, 551–560 (2001)
Parlitz, U., Kocarev, L., Stojanovski, T., Junge, L.: Chaos synchronization using sporadic driving. Physica D 109, 139–152 (1997)
Yang, T.: Impulsive Systems and Control: Theory and Application. Nova Science, Huntington (2001)
Li, C.D., Liao, X.F., Zhang, R.: Impulsive synchronization of nonlinear coupled chaotic systems. Phys. Lett. A 328, 47–50 (2004)
Haeri, M., Dehghani, M.: Impulsive synchronization of Chen’s heperchaotic system. Phys. Lett. A 356, 226–230 (2006)
Zhang, G., Liu, Z., Ma, Z.: Synchronization of complex dynamical networks via impulsive control. Chaos 17, 043126 (2007)
Newton, R.B., Leipnik, T.A.: Double strange attractors in rigid body motion with linear feedback control. Phys. Lett. A 86, 63–67 (1981)
Richter, H.: Controlling chaotic systems with multiple strange attractors. Phys. Lett. A 300, 182–188 (2002)
Wang, X., Tian, L.: Bifurcation analysis and linear control of the Newton–Leipnik system. Chaos Solitons Fractals 27, 31–38 (2006)
Ray, A., Ghosh, D., Roy Chowdhury, A.: Topological study of multiple co-existing attractor in a nonlinear system, J. Phys. A, Math. Theor. (2009, communicated)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ghosh, D., Roy Chowdhury, A. Nonlinear observer-based impulsive synchronization in chaotic systems with multiple attractors. Nonlinear Dyn 60, 607–613 (2010). https://doi.org/10.1007/s11071-009-9618-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-009-9618-5