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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 {\it R. R. Vance} and {\it 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 Second order parabolic equations, initial boundary value problems 34K13 Periodic solutions of functional differential equations
##### Keywords:
delay; positive periodic solution
Full Text:
##### References:
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