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A global stability criterion for scalar functional differential equations

E. Liz·V. Tkachenko·S. Trofimchuk
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Abstract

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.

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E. Liz, V. Tkachenko, S. Trofimchuk. 2003-04-10. A global stability criterion for scalar functional differential equations. https://arxiv.org/abs/math/0112047

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