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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 412169, 8 pages
http://dx.doi.org/10.1155/2014/412169
Research Article

Stability and Passivity of Spatially and Temporally Complex Dynamical Networks with Time-Varying Delays

1School of Computer Science & Software Engineering, Tianjin Polytechnic University, Tianjin 300387, China
2College of Post and Telecommunication of WIT, Wuhan 430070, China

Received 7 May 2014; Accepted 16 August 2014; Published 3 September 2014

Academic Editor: Zhichun Yang

Copyright © 2014 Shun-Yan Ren and Yue-Hui Zhao. 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. J. Lu and G. Chen, “A time-varying complex dynamical network model and its controlled synchronization criteria,” IEEE Transactions on Automatic Control, vol. 50, no. 6, pp. 841–846, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. W. Yu, G. Chen, and J. Lü, “On pinning synchronization of complex dynamical networks,” Automatica, vol. 45, no. 2, pp. 429–435, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. W. Yu, J. Cao, and J. Lu, “Global synchronization of linearly hybrid coupled networks with time-varying delay,” SIAM Journal on Applied Dynamical Systems, vol. 7, no. 1, pp. 108–133, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. J. L. Wang, H. N. Wu, and L. Guo, “Novel adaptive strategies for synchronization of linearly coupled neural networks with reaction-diffusion terms,” IEEE Transactions on Neural Networks and Learning Systems, vol. 25, pp. 429–440, 2014. View at Google Scholar
  5. J. L. Wang and H. N. Wu, “Synchronization and adaptive control of an array of linearly coupled reaction-diffusion neural networks with hybrid coupling,” IEEE Transactions on Cybernetics, vol. 44, no. 8, pp. 1350–1361, 2014. View at Publisher · View at Google Scholar
  6. J. L. Wang, Z. C. Yang, T. W. Huang, and M. Q. Xiao, “Synchronization criteria in complex dynamical networks with nonsymmetric coupling and multiple time-varying delays,” Applicable Analysis, vol. 91, no. 5, pp. 923–935, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. J. L. Wang, Z. C. Yang, and T. W. Huang, “Local and global exponential synchronization of complex delayed dynamical networks with general topology,” Discrete and Continuous Dynamical Systems B, vol. 16, no. 1, pp. 393–408, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. J.-L. Wang and H.-N. Wu, “Local and global exponential output synchronization of complex delayed dynamical networks,” Nonlinear Dynamics, vol. 67, no. 1, pp. 497–504, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. J. L. Wang and H. N. Wu, “Synchronization criteria for impulsive complex dynamical networks with time-varying delay,” Nonlinear Dynamics, vol. 70, no. 1, pp. 13–24, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. J. L. Wang and H. N. Wu, “Adaptive output synchronization of complex delayed dynamical networks with output coupling,” Neurocomputing, vol. 142, pp. 174–181, 2014. View at Publisher · View at Google Scholar
  11. M. D. Holland and A. Hastings, “Strong effect of dispersal network structure on ecological dynamics,” Nature, vol. 456, no. 7223, pp. 792–795, 2008. View at Publisher · View at Google Scholar · View at Scopus
  12. J. M. Montoya, S. L. Pimm, and R. V. Solé, “Ecological networks and their fragility,” Nature, vol. 442, no. 7100, pp. 259–264, 2006. View at Publisher · View at Google Scholar · View at Scopus
  13. W. Ko and I. Ahn, “Dynamics of a simple food chain model with a ratio-dependent functional response,” Nonlinear Analysis: Real World Applications, vol. 12, no. 3, pp. 1670–1680, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. Y.-M. Wang, “Asymptotic behavior of solutions for a Lotka-Volterra mutualism reaction-diffusion system with time delays,” Computers & Mathematics with Applications, vol. 58, no. 3, pp. 597–604, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. Y. M. Wang, “Asymptotic behavior of solutions for a class of predator-prey reaction-diffusion systems with time delays,” Journal of Mathematical Analysis and Applications, vol. 328, no. 1, pp. 137–150, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. C. Wang, S. Wang, F. Yang, and L. Li, “Global asymptotic stability of positive equilibrium of three-species Lotka-Volterra mutualism models with diffusion and delay effects,” Applied Mathematical Modelling, vol. 34, no. 12, pp. 4278–4288, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. C. V. Pao, “The global attractor of a competitor-competitor-mutualist reaction-diffusion system with time delays,” Nonlinear Analysis: Theory, Methods and Applications, vol. 67, no. 9, pp. 2623–2631, 2007. View at Publisher · View at Google Scholar · View at Scopus
  18. C. V. Pao, “Global attractor of a coupled finite difference reaction diffusion system with delays,” Journal of Mathematical Analysis and Applications, vol. 288, no. 1, pp. 251–273, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  19. C. V. Pao, “Convergence of solutions of reaction-diffusion systems with time delays,” Nonlinear Analysis. Theory, Methods & Applications, vol. 48, pp. 349–362, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  20. M. R. Garvie, “Finite-difference schemes for reaction-diffusion equations modeling predator-prey interactions in MATLAB,” Bulletin of Mathematical Biology, vol. 69, no. 3, pp. 931–956, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. K. I. Kim and Z. Lin, “Blowup in a three-species cooperating model,” Applied Mathematics Letters, vol. 17, no. 1, pp. 89–94, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. J. L. Wang and H. N. Wu, “Stability analysis of impulsive parabolic complex networks,” Chaos, Solitons and Fractals, vol. 44, no. 11, pp. 1020–1034, 2011. View at Publisher · View at Google Scholar · View at Scopus
  23. J. L. Wang and H. N. Wu, “Robust stability and robust passivity of parabolic complex networks with parametric uncertainties and time-varying delays,” Neurocomputing, vol. 87, pp. 26–32, 2012. View at Publisher · View at Google Scholar · View at Scopus
  24. J.-L. Wang, H.-N. Wu, and L. Guo, “Pinning control of spatially and temporally complex dynamical networks with time-varying delays,” Nonlinear Dynamics, vol. 70, no. 2, pp. 1657–1674, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  25. L. O. Chua, “Passivity and complexity,” IEEE Transactions on Circuits and Systems. I. Fundamental Theory and Applications, vol. 46, no. 1, pp. 71–82, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  26. L. Xie, M. Fu, and H. Li, “Passivity analysis and passification for uncertain signal processing systems,” IEEE Transactions on Signal Processing, vol. 46, no. 9, pp. 2394–2403, 1998. View at Publisher · View at Google Scholar · View at Scopus
  27. D. J. Hill and P. J. Moylan, “Stability results for nonlinear feedback systems,” Automatica, vol. 13, no. 4, pp. 377–382, 1977. View at Publisher · View at Google Scholar · View at Scopus
  28. G. L. Santosuosso, “Passivity of nonlinear systems with input-output feedthrough,” Automatica, vol. 33, no. 4, pp. 693–697, 1997. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  29. W. Yu, “Passive equivalence of chaos in Lorenz system,” IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 46, no. 7, pp. 876–878, 1999. View at Publisher · View at Google Scholar · View at Scopus
  30. C. W. Wu, “Synchronization in arrays of coupled nonlinear systems: passivity, circle criterion, and observer design,” IEEE Transactions on Circuits and Systems. I. Fundamental Theory and Applications, vol. 48, no. 10, pp. 1257–1261, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  31. G. Calcev, R. Gorez, and M. De Neyer, “Passivity approach to fuzzy control systems,” Automatica, vol. 34, no. 3, pp. 339–344, 1998. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  32. J. L. Wang, H. N. Wu, and L. Guo, “Passivity and stability analysis of reaction-diffusion neural networks with dirichlet boundary conditions,” IEEE Transactions on Neural Networks, vol. 22, no. 12, pp. 2105–2116, 2011. View at Publisher · View at Google Scholar · View at Scopus
  33. J. G. Lu, “Global exponential stability and periodicity of reaction-diffusion delayed recurrent neural networks with Dirichlet boundary conditions,” Chaos, Solitons and Fractals, vol. 35, no. 1, pp. 116–125, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus