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- W2120488007 abstract "The problem of global stability in scalar delay dierential equations of the form x 0 (t) = f1(x(t h))g2(x(t)) f2(x(t h))g1(x(t)) is studied. Functions fi and gi;i = 1; 2; are continuous and such that the equation assumes a unique positive equilibrium. Two types of sucient conditions for the global asymptotic stability of the unique equilibrium are established: (i) delay independent, and (ii) conditions involving the size h of the delay. Delay independent conditions make use of the global stability in the limiting (as h ! 1) dierence equation f1(xn)g2(xn+1) = f2(xn)g1(xn+1): the latter always implying the global stability in the dierential equation for all values of the delay h 0. The delay dependent conditions involve the global attractivity property in specially constructed one-dimensional maps (dierence equations) that include the nonlinearities fi and gi, and the delay h. AMS (MOS) 2001 Subject Classications: 34K20, 92D25" @default.
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- W2120488007 date "2003-01-01" @default.
- W2120488007 modified "2023-09-27" @default.
- W2120488007 title "Global Stability of a Class of Scalar Nonlinear Delay Dierential Equations" @default.
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