Time lags in a “food-limited” population model. (English) Zbl 0639.34070

We obtain sufficient and necessary and sufficient conditions for the oscillation of all positive solutions of \[ \dot N(t)=rN(t)(K-N(t- \tau))/(K+rcN(t-\tau)), \] where r,K,\(\tau\) \(\in (0,\infty)\) and \(c\in [0,\infty)\). We also obtain sufficient conditions for the global attractivity of the positive equilibrium K.
Reviewer: K.Gopalsamy


34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
92D25 Population dynamics (general)
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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[1] Barbalat I., Rev. Roumaine Math. Pures Appl 4 pp 267– (1959)
[2] DOI: 10.1111/j.1749-6632.1948.tb39854.x
[3] DOI: 10.1016/0022-247X(62)90041-0 · Zbl 0106.29503
[4] Kakutani S., On the nonlinear difference-differential equation yf(t) = [A - By(t - x)]y(t) in contributions to the theory of nonlinear oscillations, IV (1958)
[5] Kulenovic M.R.S., Quart. Appl. Math 45 pp 155– (1987)
[6] Kulenovic M.R.S., Bull. Math. Biol 49 pp 615– (1987) · Zbl 0634.92013
[7] DOI: 10.1071/ZO9540009
[8] Smith F.E., Ecology 194 pp 66– (1955)
[9] DOI: 10.1515/crll.1955.194.66 · Zbl 0064.34203
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