Convergence of Solutions for an Equation with State-Dependent Delay

A result of Smith and Thieme shows that if a semiflow is strongly order preserving, then a typical orbit converges to the set of equilibria. For the equation with state-dependent delay ˙xŽt. xŽt. fŽxŽt rŽxŽt...., where 0 and f and r are smooth real functions with fŽ0. 0 and f 0, we construct a semiflow which is monotone but not strongly order preserving. We prove a convergence result under a monotonicity condition different from the strong order preserving property, and apply it to the above equation to obtain generic convergence