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Periodic solutions for a semi-ratio-dependent predator-prey dynamical system with a class of functional responses on time scales. (English) Zbl 1149.34029
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.
MSC:
34C25Periodic solutions of ODE
92D25Population dynamics (general)
47N20Applications of operator theory to differential and integral equations
39A10Additive difference equations