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On a periodic predator-prey system with time delays on time scales. (English) Zbl 1221.34179

Summary: With the help of a continuation theorem based on [R. Gaines and J. L. Mawhin, Coincidence degree and nonlinear differential equations. Lecture Notes in Mathematics 568, Springer-Verlag (1977; Zbl 0339.47031)] coincidence degree theory, easily verifiable criteria are established for the global existence of positive periodic solutions of the predator-prey system with time delays on time scales, given by

x 1 Δ (t)=a 1 (t)-b 1 (t)exp{x 1 (t-τ 1 (t))}-c(t)exp{x 2 (t-τ 2 (t))} 1-mexp{x 1 (t)},x 2 Δ (t)=-a 2 (t)+b 2 (t)exp{x 1 (t-τ 2 (t))} 1-mexp{x 1 (t-τ 2 (t))},

where a i ,b i ,c,τ i C(𝕋, + ), i=1,2, are T-periodic functions.

34K13Periodic solutions of functional differential equations
34N05Dynamic equations on time scales or measure chains
92D25Population dynamics (general)