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International Journal of Differential Equations
Volume 2017, Article ID 1946304, 7 pages
https://doi.org/10.1155/2017/1946304
Research Article

Finite Time Synchronization of Extended Nonlinear Dynamical Systems Using Local Coupling

1School of Mathematical Sciences and Information Technology, Department of Mathematics, Yachay Tech, Urcuqui, Ecuador
2Facultad de Ingeniería en Ciencias Aplicadas, Universidad Técnica del Norte, Ibarra, Ecuador
3Departamento de Estadística, Facultad de Ciencias Económicas y Sociales, Universidad Central de Venezuela, Caracas, Venezuela

Correspondence should be addressed to P. García; ce.ude.ntu@aicragp

Received 21 July 2017; Accepted 14 November 2017; Published 7 December 2017

Academic Editor: Peiguang Wang

Copyright © 2017 A. Acosta 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

  1. H. Fujisaka and T. Yamada, “Stability theory of synchronized motion in coupled-oscillator systems,” Progress of Theoretical and Experimental Physics, vol. 69, no. 1, pp. 32–47, 1983. View at Publisher · View at Google Scholar · View at MathSciNet
  2. L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems,” Physical Review Letters, vol. 64, no. 8, pp. 821–824, 1990. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. B. Jovic, Synchronization Techniques for Chaotic Communication Systems, Springer, Berlin, Germany, 2001.
  4. S. Boccaletti, J. Kurths, G. Osipov, D. L. Valladares, and C. S. Zhou, “The synchronization of chaotic systems,” Physics Reports, vol. 366, no. 1-2, pp. 1–101, 2002. View at Publisher · View at Google Scholar · View at Scopus
  5. L. Pecora, T. Carroll, G. Johnson, D. Mar, and K. S. Fink, “Synchronization stability in coupled oscillator arrays: solution for arbitrary configurations,” International Journal of Bifurcation and Chaos, vol. 10, no. 2, pp. 273–290, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. L. Kocarev, Z. Tasev, and U. Parlitz, “Synchronizing spatiotemporal chaos of partial differential equations,” Physical Review Letters, vol. 79, no. 1, pp. 51–54, 1997. View at Publisher · View at Google Scholar · View at Scopus
  7. A. Acosta, P. Garca, and H. Leiva, “Synchronization of non-identical extended chaotic systems,” Applicable Analysis: An International Journal, vol. 92, no. 4, pp. 740–751, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  8. L. Xie and Y. Zhao, “Synchronization of some kind of PDE chaotic systems by invariant manifold method,” International Journal of Bifurcation and Chaos, vol. 5, no. 7, pp. 2303–2309, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  9. P. García, A. Acosta, and H. Leiva, “Synchronization conditions for master-slave reaction diffusion systems,” Europhysics Letters, vol. 88, no. 6, pp. 60006-1–60006-6, 2009. View at Publisher · View at Google Scholar
  10. Z. Xu and W. Jiangsum, “Synchronization of two discrete Ginzburg-Landau equations using local coupling,” International Journal of Nonlinear Science, vol. 1, no. 1, pp. 19–29, 2006. View at Google Scholar
  11. R. O. Grigoriev and A. Handel, “Non-normality and the localized control of extended systems,” Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, vol. 66, no. 6, Article ID 067201, pp. 067201/1–067201/4, 2002. View at Publisher · View at Google Scholar · View at Scopus
  12. K. Wu and B.-S. Chen, “Synchronization of partial differential systems via diffusion coupling,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 59, no. 11, pp. 2655–2668, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. P. Gray and S. K. Scott, “Sustained oscillations and other exotic patterns of behavior in isothermal reactions,” The Journal of Physical Chemistry, vol. 89, no. 1, pp. 22–32, 1985. View at Publisher · View at Google Scholar
  14. D. Henry, Geometric Theory of Semilinear Parabolic Equations, vol. 840 of Lecture Notes in Mathematics, Springer, New York, NY, USA, 1981.
  15. G. R. Sell and Y. You, Dynamics of evolutionary equations, vol. 143 of Applied Mathematical Sciences, Springer, 2002. View at Publisher · View at Google Scholar · View at MathSciNet