A global stability criterion for scalar functional differential equations

Details A global stability criterion for scalar functional differential equations A global stability criterion for scalar functional differential equations

2001-12-05

arxiv.org/abs/math/0112047v2

Mathematics

Dynamical Systems

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

Scientific paper

We consider scalar delay differential equations $x'(t) = -\delta x(t) + f(t,x_t) (*)$ 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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