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Periodic solutions of competition Lotka-Volterra dynamic system on time scales. (English) Zbl 1186.34129
Summary: We rigorously establish an existence theorem of periodic solutions for the competition of Lotka-Volterra dynamic systems with a time delay and diffusion on time scales. It is shown that the existence of periodic solutions depend on the parameters of the model. It is also shown that a known result in the literature can can carry over quite easily to its discrete counterpart, and a much more accurate result can be obtained when studying the dynamic system on time scales. Moreover, one example is given to illustrate the result obtained.
MSC:
34N05Dynamic equations on time scales or measure chains
37N25Dynamical systems in biology
92D25Population dynamics (general)
34C25Periodic solutions of ODE
34C60Qualitative investigation and simulation of models (ODE)
39A10Additive difference equations
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