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Zbl 1149.34029
Fazly, Mostafa; Hesaaraki, Mahmoud
Periodic solutions for a semi-ratio-dependent predator-prey dynamical system with a class of functional responses on time scales. (English)
[J] Discrete Contin. Dyn. Syst., Ser. B 9, No. 2, 267-279 (2008). ISSN 1531-3492; ISSN 1553-524X/e

The authors investigate time-periodic, semi-ratio-dependent predator-prey systems with rather general and not necessarily monotonous functional responses, on socalled time scales that were introduced by S. Hilger some twenty years ago. Their objective is to improve and extend several results on the existence of at least one periodic solution which had been obtained earlier by different authors. As the main tool of proof, the present authors use a continuation theorem by Gaines and Mawhin on certain nonlinear operator equations in Banach spaces, involving Fredholm operators of index zero and topological degree theory.
[Josef Hainzl (Freiburg)]

MSC 2000:: *34C25 Periodic solutions of ODE
92D25 Population dynamics
47N20 Appl. of operator theory to differential and integral equations
39A10 Difference equations

Keywords: predator-prey system; periodic solution; time scales

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