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On neutral delay logistic Gause-type predator-prey systems. (English) Zbl 0728.92016
Summary: The qualitative behaviour of solutions of the neutral delay logistic Gause-type predator-prey system \[ (*)\quad \dot x(t)=rx(t)[1-(x(t- \mu)+\rho \dot x(t-\tau))/K]-y(t)p(x(t)),\quad \dot y(t)=y(t)[-\alpha +\beta p(x(t-\sigma))] \] is investigated. Sufficient conditions are obtained for the local asymptotic stability of the positive steady state of (*). In fact, some of these sufficient conditions are also necessary except at these critical values. Results on the oscillatory and non- oscillatory characteristics of the positive solutions of (*) are also included.

MSC:
92D25 Population dynamics (general)
34D05 Asymptotic properties of solutions to ordinary differential equations
34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
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