## An asymptotic stability result for scalar delayed population models

HTML articles powered by AMS MathViewer

- by Teresa Faria PDF
- Proc. Amer. Math. Soc.
**132**(2004), 1163-1169 Request permission

## 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

- T. Faria, Global attractivity in scalar delayed differential equations with applications to population models, to appear in J. Math. Anal. Appl.
- Yang Kuang,
*Delay differential equations with applications in population dynamics*, Mathematics in Science and Engineering, vol. 191, Academic Press, Inc., Boston, MA, 1993. MR**1218880** - Ming Po Ch’ên, J. S. Yu, X. Z. Qian, and Z. C. Wang,
*On the stability of a delay differential population model*, Nonlinear Anal.**25**(1995), no. 2, 187–195. MR**1333822**, DOI 10.1016/0362-546X(94)00199-R - Joseph W.-H. So and J. S. Yu,
*Global stability for a general population model with time delays*, Differential equations with applications to biology (Halifax, NS, 1997) Fields Inst. Commun., vol. 21, Amer. Math. Soc., Providence, RI, 1999, pp. 447–457. MR**1662633** - Joseph W.-H. So, J. S. Yu, and Ming-Po Chen,
*Asymptotic stability for scalar delay differential equations*, Funkcial. Ekvac.**39**(1996), no. 1, 1–17. MR**1401650** - R. R. Vance and E. A. Coddington,
*A nonautonomous model of population growth*, J. Math. Biol.**27**(1989), no. 5, 491–506. MR**1015008**, DOI 10.1007/BF00288430 - Toshiaki Yoneyama,
*On the ${3\over 2}$ stability theorem for one-dimensional delay-differential equations*, J. Math. Anal. Appl.**125**(1987), no. 1, 161–173. MR**891356**, DOI 10.1016/0022-247X(87)90171-5 - Toshiaki Yoneyama,
*The $3/2$ stability theorem for one-dimensional delay-differential equations with unbounded delay*, J. Math. Anal. Appl.**165**(1992), no. 1, 133–143. MR**1151064**, DOI 10.1016/0022-247X(92)90071-K - James A. Yorke,
*Asymptotic stability for one dimensional differential-delay equations*, J. Differential Equations**7**(1970), 189–202. MR**252799**, DOI 10.1016/0022-0396(70)90132-4

## 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
- 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
- © Copyright 2003 American Mathematical Society
- 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
- MathSciNet review: 2045433