Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

Remarks on a variant of Lyapunov-LaSalle theorem

1 School of Science, Beijing University of Civil Engineering and Architecture, Beijing 102616, P.R. China
2 School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, P.R. China

The aim of this paper is to give some global stability criteria on a variant of Lyapunov-LaSalle theorem for a class of delay di erential system.
  Figure/Table
  Supplementary
  Article Metrics

Keywords delay differential equations; Lyapunov-LaSalle theorem; global stability

Citation: Songbai Guo, Wanbiao Ma. Remarks on a variant of Lyapunov-LaSalle theorem. Mathematical Biosciences and Engineering, 2019, 16(2): 1056-1066. doi: 10.3934/mbe.2019050

References

  • 1. W. Cheng, W. Ma and S. Guo, A class of virus dynamic model with inhibitory effect on the growth of uninfected T cells caused by infected T cells and its stability analysis, Commun. Pur. Appl. Anal., 15 (2016), 795-806.
  • 2. Y. Enatsu, Y. Nakata and Y. Muroya, Lyapunov functional techniques for the global stability analysis of a delayed SIRS epidemic model, Nonlinear Anal-Real, 13 (2012), 2120-2133.
  • 3. S. Guo and W. Ma, Global behavior of delay differential equations model of HIV infection with apoptosis, Discrete Contin. Dyn. Syst.-Ser. B, 21 (2016), 103-119.
  • 4. S. Guo and W. Ma, Global dynamics of a microorganism flocculation model with time delay, Commun. Pur. Appl. Anal., 16 (2017), 1883-1891.
  • 5. S. Guo, W. Ma and X.-Q. Zhao, Global dynamics of a time-delayed microorganism flocculation model with saturated functional responses, J. Dyn. Differ. Equ., 30 (2018), 1247-1271.
  • 6. J. K. Hale, Theory of Functional Differential Equations, Springer-Verlag, New York, 1977.
  • 7. A. V. M. Herz, S. Bonhoeffer, R. M. Anderson, R. M. May and M. A. Nowak, Viral dynamics in vivo: Limitations on estimates of intracellular delay and virus decay, Proc. Natl. Acad. Sci. USA, 93 (1996), 7247-7251.
  • 8. S.-B. Hsu, Limiting behavior for competing species, SIAM J. Appl. Math., 34 (1978), 760-763.
  • 9. S.-B. Hsu, A survey of constructing Lyapunov functions for mathematical models in population biology, Taiwan. J. Math., 9 (2005), 151-173.
  • 10. G. Huang, Y. Takeuchi and W. Ma, Lyapunov functionals for delay differential equations model of viral infections, SIAM J. Appl. Math., 70 (2010), 2693-2708.
  • 11. Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, Boston, 1993.
  • 12. A. Korobeinikov, Lyapunov functions and global stability for SIR, SIRS, and SIS epidemiological models, Appl. Math. Lett., 15 (2002), 955-960.
  • 13. X. Liao, Theory Methods and Application of Stability, 2nd ed., Huazhong University of Science and Technology Press, Wuhan, 2010. (in Chinese)
  • 14. C. C. McCluskey, Using Lyapunov functions to construct Lyapunov functionals for delay differential equations, SIAM J. Appl. Dyn. Syst., 14 (2015), 1-24.
  • 15. Y. Saito, T. Hara and W. Ma, Necessary and sufficient conditions for permanence and global stability of a Lotka-Volterra system with two delays, J. Math. Anal. Appl., 236 (1999), 534-556.
  • 16. K. Song, W. Ma, S. Guo and H. Yan, A class of dynamic model describing microbial flocculant with nutrient competition and metabolic products in wastewater treatment, Adv. Differ. Equ., 2018 (2018), 33.
  • 17. S. Tang, W. Ma and P. Bai, A novel dynamic model describing the spread of the MERS-CoV and the expression of dipeptidyl peptidase 4, Comput. Math. Method. M., 2017 (2017), 5285810.
  • 18. W. Wang, W. Ma and H. Yan, Global Dynamics of Modeling Flocculation of Microorganism, Appl. Sci., 6 (2016), 221.
  • 19. G. S. K. Wolkowicz and Z. Lu, Global dynamics of a mathematical model of competition in the chemostat: general response functions and differential death rates, SIAM J. Appl. Math., 52 (1992), 222-233.
  • 20. T. Zhang, X. Meng and T. Zhang, Global dynamics of a virus dynamical model with cell-to-cell transmission and cure rate, Comput. Math. Method. M., 2015 (2015), 758362.
  • 21. T. Zhang, X. Meng and T. Zhang, Global analysis for a delayed SIV model with direct and environmental transmissions, J. Appl. Anal. Comput., 6 (2016), 479-491.

 

Reader Comments

your name: *   your email: *  

© 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved