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Asymptotic stability for delayed logistic type equations. (English) Zbl 1145.34043

The author considers a general delayed logistic equation
\[ x'(t)= b(t)x(t)[1- L(x_t)], \]
where \(L: C(-r; 0;\mathbb{R})\to\mathbb{R}\) is a bounded linear operator, \(x_t(s)= x(t+ s)\) and \(b\) is a positive continuous function.
The global asymptotic stability of the positive equilibrium is proven under some condition on a negative feedback term without delay dominating the delayed effect.
In the last section the global stability of more general scalar delay differential equations is studied.

MSC:

34K20 Stability theory of functional-differential equations
92D25 Population dynamics (general)
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References:

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