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Dynamics of a plant-herbivore model with differential-difference equations. (English) Zbl 1438.92068

Summary: 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 a certain regions.

MSC:

92D25 Population dynamics (general)
39A28 Bifurcation theory for difference equations
39A30 Stability theory for difference equations
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