A global stability criterion for scalar functional differential equations
| dc.creator | Liz, E. | |
| dc.creator | Tkachenko, V. | |
| dc.creator | Trofimchuk, S. | |
| dc.date | 2001-12-05 | |
| dc.date | 2003-04-10 | |
| dc.date.accessioned | 2026-07-07T04:45:00Z | |
| dc.date.available | 2026-07-07T04:45:00Z | |
| dc.description | We consider scalar delay differential equations $x'(t) = -δx(t) + f(t,x_t) (*)$ with nonlinear f satisfying a sort of negative feedback condition combined with a boundedness condition. The well known Mackey-Glass type equations, equations satisfying the Yorke condition, equations with maxima are kept within our considerations. Here, we establish a criterion for the global asymptotical stability of a unique steady state to $(*)$. As an example, we study Nicholson's blowflies equation, where our computations support Smith's conjecture about the equivalence of global and local asymptotical stability in this population model. | |
| dc.description | 28 pages, 2 figures. Final version, to appear in the SIAM Journal on Mathematical Analysis | |
| dc.identifier | https://arxiv.org/abs/math/0112047 | |
| dc.identifier | http://arxiv.org/abs/math/0112047 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62822 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 34K20; 92D25 | |
| dc.title | A global stability criterion for scalar functional differential equations | |
| dc.type | text |