Impulse Effect on the Food-Limited Population Model with Piecewise Constant Argument

The qualitative study of mathematical models is an important area in applied mathematics. In this paper, a version of the food-limited population model with piecewise constant argument under impulse effect is investigated. Differential equations with piecewise constant arguments are related to difference equations. First, a representation for the solutions of the food-limited population model is stated in terms of the solutions of corresponding difference equation. Then using linearized oscillation theory for difference equations, a sufficient condition for the oscillation of the solutions about positive equilibrium point is obtained. Moreover, asymptotic behavior of the non-oscillatory solutions are investigated. Later, applying the same theory, non-impulsive model is also studied. Numerical examples are given to compare the results of impulsive model with the results of nonimpulsive case. The results show that when the solutions of impulsive differential equation model are oscillatory about positive equilibrium under suitable conditions the solutions of the corresponding non-impulsive model is not oscillatory. This situation indicates to the importance of impulse effects on the asymptotic behavior of the solutions