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Positive periodic solutions for a class of neutral delay gause-type predator-prey system. (English) Zbl 1181.34089

By using the continuation theorem from coincidence degree theory, the authors establish an existence theorem for positive periodic solutions of the following neutral delay Gause-type predator-prey system

x ' (t)=x(t)[r(t)-a(t)x(t-σ 1 )-ρx ' (t-σ 2 )]-φ(t,x(t))y(t-τ 1 (t)),y ' (t)=y(t)[-d(t)+h(t,x(t-τ 2 (t))]·

The technique is standard, and the key point is an a priori estimate of the bound for the solutions of the system.

MSC:
34K60Qualitative investigation and simulation of models
34K13Periodic solutions of functional differential equations
92D25Population dynamics (general)
34K40Neutral functional-differential equations
47N20Applications of operator theory to differential and integral equations