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Almost-periodic solutions of a delay population equation with feedback control. (English) Zbl 1128.34045
Consider the delay differential system $$\align\frac{dx}{dt}(t) & = x(t)[r(t)-a(t)x(t)-x(t-\tau)-c(t)u(t)],\\ \frac{du}{dt}(t) & =-\eta(t)u(t)+g (t)x(t-\tau), \tag *\endalign$$ where $\tau>0$, the functions $r,a,c,\eta$ and $g$ are almost-periodic. The authors derive conditions ensureing a unique almost periodic solution with the properties: (i) All components are positive for all time. (ii) It is uniformly asymptotically stable. (iii) The frequency module is contained in the frequency module of $r,a,c,\eta$ and $g$.

MSC:
34K14Almost and pseudo-periodic solutions of functional differential equations
92D25Population dynamics (general)
34K35Functional-differential equations connected with control problems
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References:
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