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Stable steady state of some population models. (English) Zbl 0744.34071
Applying an analytical method and limiting equations arguments, some sufficient conditions are provided for the existence of a unique positive equilibrium $K$ for the equation (1) $\dot x(t)=-\gamma x(t)+D(x\sb t)$ which is the general form of many population models. The authors also investigate when an equilibrium for the functional differential equation (1) is uniformly stable, asymptotically stable, or uniformly asymptotically stable. Applications of the results to some population models are also presented.
Reviewer: S.Anita (Iaşi)

34K20Stability theory of functional-differential equations
34K25Asymptotic theory of functional-differential equations
92D25Population dynamics (general)
Full Text: DOI
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