- Access by Xinjiang University
Synchronization of time-delayed systems
Phys. Rev. E 76, 036212 – Published 21 September, 2007Erratum Phys. Rev. E 76, 059905 (2007)
DOI: https://doi.org/10.1103/PhysRevE.76.036212
Abstract
In this paper we study synchronization in linearly coupled time-delayed systems. We first consider coupled nonidentical Ikeda systems with a square wave coupling rate. Using the theory of the time-delayed equation, we derive less restrictive synchronization conditions than those resulting from the Krasovskii-Lyapunov theory [Yang Kuang, Delay Differential Equations (Academic Press, New York, 1993)]. Then we consider a wide class of nonlinear nonidentical time-delayed systems. We also propose less restrictive synchronization conditions in an approximative sense, even if the coefficients in the linear time-delayed equation on the synchronization error are time dependent. Theoretical analysis and numerical simulations fully verify our main results.
Erratum
Erratum: Synchronization of time-delayed systems [Phys. Rev. E 76, 036212 (2007)]
Article Text
References (17)
- J. K. Hale and S. M. V. Lunel, Introduction to Functional Differential Equations (Springer, New York, 1993).
- M. C. Mackey and L. Glass, Science 197, 287 (1977).
- J. D. Farmer, Physica D 4, 366 (1982).
- B. Dorizzi, B. Grammaticos, M. Le Berre, Y. Pomeau, E. Ressayre, and A. Tallet, Phys. Rev. A 35, 328 (1987); K. Ikeda and K. Matsumoto, Physica D 29, 223 (1987).
- S. Boccaletti, J. Kurths, G. Osipov, D. L. Valladares, and C. Zhou, Phys. Rep. 366, 1 (2002); R. He and P. G. Vaidya, Phys. Rev. E 59, 4048 (1999); S. Sano, A. Uchida, S. Yoshimori, and R. Roy, ibid. 75, 016207 (2007).
- K. Pyragas, Phys. Rev. E 58, 3067 (1998).
- A. S. Landsman and I. B. Schwartz, Phys. Rev. E 75, 026201 (2007).
- D. V. Senthilkumar, M. Lakshmanan, and J. Kurths, Phys. Rev. E 74, 035205(R) (2006).
- H. U. Voss, Phys. Rev. E 61, 5115 (2000).
- E. M. Shahverdiev and K. A. Shore, Phys. Rev. E 71, 016201 (2005).
- E. M. Shahverdiev, S. Sivaprakasam, and K. A. Shore, Phys. Rev. E 66, 017204 (2002); E. M. Shahverdiev, ibid. 70, 067202 (2004); D. V. Senthilkumar and M. Lakshmanan, ibid. 71, 016211 (2005).
- S. B. Zhou, H. Li, and Z. F. Wu, Phys. Rev. E 75, 037203 (2007).
- Yang Kuang, Delay Differential Equations (Academic Press, London, 1993).
- V. Lakshmikantham and S. Leela, Differential and Integral Inequalities (Academic Press, New York, 1969).
- A. Hmamed, Int. J. Syst. Sci. 22, 605 (1991); J.-S. Chiou, IEE Proc.: Control Theory Appl. 153, 684 (2006).
- N. F. Rulkov, M. M. Sushchik, L. S. Tsimring, and H. D. I. Abarbanel, Phys. Rev. E 51, 980 (1995); M. Zhan, X. Wang, X. Gong, G. W. Wei, and C.-H. Lai, ibid. 68, 036208 (2003).
- L. F. Shampine and S. Thompson, Appl. Numer. Math. 37, 441 (2001).