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Linearized Stability for a New Class of Neutral Equations with State-Dependent Delay

Abstract

For neutral delay differential equations of the form x˙(t)=g(∂xt,xt), with g defined on an open subset of the space C([−h,0],Rn)×C1([−h,0],Rn), we extend an earlier principle of linearized stability. The present result applies to a wider class of neutral differential equations x˙(t)=f(x(t),x˙(t−τ(x(t))),x(t−σ(x(t)))) with state-dependent delays which includes models for population dynamics with maturation delay.

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