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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 210156, 10 pages
Finite-Time Attractivity for Diagonally Dominant Systems with Off-Diagonal Delays
1Department of Mathematics, Imperial College London, London SW7 2AZ, UK
2Institute of Mathematics, Vietnam Academy of Science and Technology, Hanoi 10307, Vietnam
3Center for Dynamics, TU Dresden, 01062 Dresden, Germany
Received 23 April 2012; Accepted 6 June 2012
Academic Editor: Agacik Zafer
Copyright © 2012 T. S. Doan and S. Siegmund. 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.
- A. Berger, D. T. Son, and S. Siegmund, “Nonautonomous finite-time dynamics,” Discrete and Continuous Dynamical Systems. Series B, vol. 9, no. 3-4, pp. 463–492, 2008.
- G. Haller, “A variational theory of hyperbolic Lagrangian Coherent Structures,” Physica D, vol. 240, no. 7, pp. 574–598, 2011.
- S. C. Shadden, F. Lekien, and J. E. Marsden, “Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows,” Physica D, vol. 212, no. 3-4, pp. 271–304, 2005.
- A. Berger, T. S. Doan, and S. Siegmund, “A definition of spectrum for differential equations on finite time,” Journal of Differential Equations, vol. 246, no. 3, pp. 1098–1118, 2009.
- M. Branicki and S. Wiggins, “Finite-time Lagrangian transport analysis: stable and unstable manifolds of hyperbolic trajectories and finite-time Lyapunov exponents,” Nonlinear Processes in Geophysics, vol. 17, no. 1, pp. 1–36, 2010.
- T. S. Doan, K. Palmer, and S. Siegmund, “Transient spectral theory, stable and unstable cones and Gershgorin's theorem for finite-time differential equations,” Journal of Differential Equations, vol. 250, no. 11, pp. 4177–4199, 2011.
- T. S. Doan, D. Karrasch, T. Y. Nguyen, and S. Siegmund, “A unified approach to finite-time hyperbolicity which extends finite-time Lyapunov exponents,” Journal of Differential Equations, vol. 252, no. 10, pp. 5535–5554, 2012.
- L. H. Duc and S. Siegmund, “Hyperbolicity and invariant manifolds for planar nonautonomous systems on finite time intervals,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 18, no. 3, pp. 641–674, 2008.
- M. Rasmussen, “Finite-time attractivity and bifurcation for nonautonomous differential equations,” Differential Equations and Dynamical Systems, vol. 18, no. 1-2, pp. 57–78, 2010.
- P. Giesl and M. Rasmussen, “Areas of attraction for nonautonomous differential equations on finite time intervals,” Journal of Mathematical Analysis and Applications, vol. 390, no. 1, pp. 27–46, 2012.
- F. Amato, M. Ariola, M. Carbone, and C. Cosentino, “Finite-time control of linear systems: a survey,” in Current Trends in Nonlinear Systems and Control, Systems & Control: Foundations & Applications, pp. 195–213, Birkhäuser, Boston, Mass, USA, 2006.
- P. Dorato, “An overview of finite-time stability,” in Current Trends in Nonlinear Systems and Control, Systems & Control: Foundations & Applications, pp. 185–194, Birkhäuser, Boston, Mass, USA, 2006.
- J. Hofbauer and J. W.-H. So, “Diagonal dominance and harmless off-diagonal delays,” Proceedings of the American Mathematical Society, vol. 128, no. 9, pp. 2675–2682, 2000.
- A. M. Fink, Almost Periodic Differential Equations, vol. 377 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1974.