A global stability criterion for scalar functional differential equations

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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.
28 pages, 2 figures. Final version, to appear in the SIAM Journal on Mathematical Analysis

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Dynamical Systems, 34K20; 92D25

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http://salesiana.dossiersoluciones.com/handle/123456789/62822

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0112047
 http://arxiv.org/abs/math/0112047

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arXiv