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Zbl 1181.34089
Liu, Guirong; Yan, Weiping; Yan, Jurang
Positive periodic solutions for a class of neutral delay gause-type predator-prey system.
(English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 10, A, 4438-4447 (2009). ISSN 0362-546X

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.
[Peixuan Weng (Guangzhou)]
MSC 2000:
*34K60 Applications of functional-differential equations
34K13 Periodic solutions of functional differential equations
92D25 Population dynamics
34K40 Neutral equations
47N20 Appl. of operator theory to differential and integral equations

Keywords: predator-prey system; periodic solution; coincidence degree; neutral functional differential equation

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