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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 $$\cases x^{\prime}(t)=x(t)[r(t)-a(t)x(t-\sigma_1)-\rho x^{\prime}(t-\sigma_2)]-\phi(t,x(t))y(t-\tau_1(t)),\\ y^{\prime}(t)=y(t)[-d(t)+h(t,x(t-\tau_2(t))]. \endcases$$ 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
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References:
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