Dynamics of a plant-herbivore model with differential-difference equations

Abstract

This paper studies the behavior of a plant–herbivore model including both differential and difference equations. To analyze global behavior of the model, we consider the solution of the system in a certain subinterval which gives to system of difference equations. The boundedness characters, the periodic nature, both local and global stability conditions of the plant–herbivore system are investigated. Numerical studies indicate that the system exhibits Neimark–Sacker bifurcation for different parameter values in certain regions.