Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

An asymptotic stability result for scalar delayed population models


Author: Teresa Faria
Journal: Proc. Amer. Math. Soc. 132 (2004), 1163-1169
MSC (2000): Primary 34K20, 34K25
DOI: https://doi.org/10.1090/S0002-9939-03-07237-X
Published electronically: August 21, 2003
MathSciNet review: 2045433
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We give sufficient conditions for the global asymptotic stability of the scalar delay differential equation $\dot x(t)=(1+x(t))F(t,x_t)$, without assuming that zero is a solution. A result of Yorke (1970) is revisited.


References [Enhancements On Off] (What's this?)

  • 1. T. Faria, Global attractivity in scalar delayed differential equations with applications to population models, to appear in J. Math. Anal. Appl.
  • 2. Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, Boston, MA, 1993. MR 94f:34001
  • 3. J. W.-H. So and J. S. Yu, Global attractivity for a population model with time delay, Proc. Amer. Math. Soc. 123 (1995), 2687-2694. MR 96c:34170a
  • 4. J. W.-H. So and J. S. Yu, Global stability for a general population model with time delays, Fields Institute Communications 21, Amer. Math. Soc., Providence, RI, 1999, pp. 447-457. MR 99m:92039
  • 5. J. W.-H. So, J. S. Yu and M.-P. Chen, Asymptotic stability for scalar delay differential equations, Funkcial. Ekvac. 39 (1996), 1-17. MR 97f:34056
  • 6. R. R. Vance and E. A. Coddington, A nonautonomous model of population growth, J. Math. Biol. 27 (1989), 491-506. MR 90j:92028
  • 7. T. Yoneyama, On the $3/2$ stability theorem for one-dimensional delay-differential equations, J. Math. Anal. Appl. 125 (1987), 161-173. MR 88e:34139
  • 8. T. Yoneyama, The $3/2$ stability theorem for one-dimensional delay-differential equations with unbounded delay, J. Math. Anal. Appl. 165 (1992), 133-143. MR 94f:34158
  • 9. J. A. Yorke, Asymptotic stability for one dimensional differential-delay equations, J. Differential Equations 7 (1970), 189-202. MR 40:6016

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 34K20, 34K25

Retrieve articles in all journals with MSC (2000): 34K20, 34K25


Additional Information

Teresa Faria
Affiliation: Departamento de Matemática, Faculdade de Ciências, and CMAF, Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal
Email: tfaria@lmc.fc.ul.pt

DOI: https://doi.org/10.1090/S0002-9939-03-07237-X
Received by editor(s): December 18, 2002
Published electronically: August 21, 2003
Additional Notes: This work was partially supported by FCT (Portugal) under CMAF and project POCTI/ 32931/MAT/2000.
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2003 American Mathematical Society

American Mathematical Society