On the problem of linearization for state-dependent delay differential equations
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- by Kenneth L. Cooke and Wenzhang Huang PDF
- Proc. Amer. Math. Soc. 124 (1996), 1417-1426 Request permission
Abstract:
The local stability of the equilibrium for a general class of state-dependent delay equations of the form \[ \dot x(t)=f\left (x_t, \int ^0_{-r_0} d\eta (s)g(x_t(-\tau (x_t)+s))\right )\] has been studied under natural and minimal hypotheses. In particular, it has been shown that generically the behavior of the state-dependent delay $\tau$ (except the value of $\tau )$ near an equilibrium has no effect on the stability, and that the local linearization method can be applied by treating the delay $\tau$ as a constant value at the equilibrium.References
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Additional Information
- Kenneth L. Cooke
- Affiliation: Department of Mathematics, Pomona College, Claremont, California 91711
- Email: kcooke@pomona.edu
- Wenzhang Huang
- Affiliation: Department of Mathematics, University of Alabama in Huntsville, Huntsville, Alabama 35899
- Email: huang@math.uah.edu
- Received by editor(s): December 3, 1993
- Additional Notes: The first author’s research was supported in part by NSF grant DMS 9208818
The second author’s research was supported in part by NSF grant DEB 925370 to Carlos Castillo-Chavez and by the U.S. Army Research Office through the Mathematical Science Institute of Cornell University - Communicated by: Hal L. Smith
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 1417-1426
- MSC (1991): Primary 34K20
- DOI: https://doi.org/10.1090/S0002-9939-96-03437-5
- MathSciNet review: 1340381