Abstract

The problem of global stability in scalar delay differential equations of the form x/spl dot/(t)=f(x(t-/spl tau/))-g(x(t)) is studied. Functions f and g are continuous and such that the equation assumes a unique equilibrium. Two types of the sufficient conditions for the global asymptotic stability of the unique equilibrium are established: (i) delay independent, and (ii) conditions involving the size /spl tau/ of the delay. Delay independent stability conditions make use of the global stability in the limiting (as /spl tau//spl rarr//spl infin/) difference equation g(x/sub n+1/)=f(x/sub n/): the latter always implying the global stability in the differential equation for all values of the delay /spl tau//spl ges/0. The delay dependent conditions involve the global attractivity in specially constructed one-dimensional maps (difference equations) that include the nonlinearities f and g, and the delay /spl tau/.

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