Classical theory has led us to believe that where more grazing is available herbivores will inflict heavier pressure on the grass, thus keeping its height low. This approach is hotly debated, although still widely accepted. Based on field data collected, van der Koppel et al. [van der Koppel, J., Huisman, J., van der Wal, R., Olff, H., 1996. Patterns of herbivory along a productivity gradient: an empirical and theoretical investigation. Ecology 77, 736-745] contest the standard plant-herbivore models, arguing that herbivores do not 'control' the plant growth entirely, and propose two differential equation models. In this paper we describe briefly how van der Koppel et al. (1996) derive their uncontrolled plant-herbivore interaction models, and then expand on the specific mathematical results cited in their paper to provide a global overview of the dynamics of such systems, for a broad range of parameter values.