zbMATH — the first resource for mathematics

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.

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)
Full Text: DOI
[1] DOI: 10.1016/0022-247X(82)90243-8 · Zbl 0492.34064
[2] Cooke K. L., Funkcialaj Ekvacioj 29 pp 77– (1986)
[3] DOI: 10.1007/978-3-642-93073-7
[4] Freedman H. I., Deterministic Mathematical Models in Population Ecology (1980) · Zbl 0448.92023
[5] Freedman H. I., Funkcialaj Ekvacioj (1991)
[6] DOI: 10.1080/02681118808806037 · Zbl 0665.34066
[7] DOI: 10.1080/00036818808839826 · Zbl 0639.34070
[8] DOI: 10.1016/0022-0396(83)90061-X · Zbl 0531.34058
[9] DOI: 10.1016/0022-0396(71)90096-9 · Zbl 0223.34057
[10] DOI: 10.1016/0022-0396(74)90080-1 · Zbl 0273.34049
[11] DOI: 10.1007/978-1-4612-9892-2
[12] DOI: 10.1016/0022-247X(91)90398-J · Zbl 0731.34089
[13] Pielou E. C., Mathematical Ecology (1977) · Zbl 0259.92001
[14] DOI: 10.2307/1933011
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.