A Note On “ Periodic Solutions Of A Three - Species Food Chain Model " [ Applied Math E - Notes , 9 ( 2009

The work of Zhang et al. [18] investigates the existence of periodic solutions in a ODE model, of a three species food chain, based on a modified Leslie-Gower scheme. They consider time dependent periodic coeffi cients to model periodicity of the natural environment. Their main result is that under certain restrictions on these coeffi cients, there exists at least one periodic solution to the three species model. In the current manuscript we prove that this result is not true. We then derive certain global existence conditions, which when enforced in conjunction with the earlier conditions of [18], yield at least one periodic solution to the model. We support all of our results via numerical simulations.