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

Gopalsamy, K.; Kulenovic, M. R. S.; Ladas, G.

Appl. Anal. 31, No. 3, 225-237 (1988).

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

MSC:

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

Keywords:

global attractivity

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