Periodic solutions of competition Lotka–Volterra dynamic system on time scales

In this paper, 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.