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Zbl 0765.34058
Gopalsamy, K.; Weng, Peixuan
Feedback regulation of logistic growth. (English)
[J] Int. J. Math. Math. Sci. 16, No.1, 177-192 (1993). ISSN 0161-1712; ISSN 1687-0425/e

The authors obtain sufficient conditions for the global asymptotic stability of the positive equilibrium of a regulated logistic growth with a delay in the state feedback of the control modeled by ${dn(t)\over dt}=rn(t)\left[1-\left({a\sb 1n(t)+a\sb 2n(t-\tau)\over K}\right)- cu(t)\right]$ ${du(t)\over dt}=-au(t)+bn(t-\tau)$. Here $u$ denotes an indirect control variable, $a\sb 1\in[0,\infty)$ and $r,a\sb 2,\tau,a,b,c\in(0,\infty)$.
[S.Anita (Iaşi)]

MSC 2000:: *34K35 Functional-differential equations connected with control problems
34K99 Functional-differential equations
34K20 Stability theory of functional-differential equations
92D25 Population dynamics
92D40 Ecology

Keywords: global asymptotic stability; regulated logistic growth; delay; state feedback; indirect control

Cited in: Zbl 1163.39011

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