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Persistence and stability in general nonautonomous single-species Kolmogorov systems with delays. (English) Zbl 1119.34056

The author studies a nonautonomous single species Kolmogorov system with delays of the type \[ \frac{dx(t)}{dt} = x(t)f(t,x_t), \;t \in [0,\infty), \]
where \(x_t (s) = x(t+s)\) \(\forall \;s \in [-\tau,0].\) This equation includes many special delayed nonautonomous population growth models of a single species. The results obtained in this paper extend the main results given by R. R. Vance and E. A. Coddington [J. Math. Biol. 27, 491–506 (1989; Zbl 0716.92016)], establishing in particular different general criteria on the boundedness, persistence, permanence, global asymptotic stability and the existence of positive periodic solutions for the equation above.

MSC:

34K25 Asymptotic theory of functional-differential equations
92D25 Population dynamics (general)
35K20 Initial-boundary value problems for second-order parabolic equations
34K13 Periodic solutions to functional-differential equations

Citations:

Zbl 0716.92016
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References:

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