Comparison principle and stability of differential equations with piecewise constant arguments

This paper studies systems of nonlinear differential equations with piecewise constant arguments (EPCA). We develop a comparison principle for this system. Then, this result is used to establish some stability properties of the system. As for the stability results we employ the Lyapunov function approach. We also show that the piecewise (constant) arguments can play as a stabilizing role in some cases where the underlying systems are unstable. A class of linear retarded EPCA are also considered in this paper. Numerical examples and an application to a single-species logistic growth model with density-dependence harvesting are given to show the effectiveness of our theoretical results.