This simple model assumes that the only limitation on the prey population size is predation and that the predator population depends solely on the number of prey available. The horizontal axis on the graph is the time axis and the vertical axis is the population size. the predator prey particle model formed using equations (1a) and (1b). We also use the boundary model to consider the case of a single predator traveling on an in nite plane of evenly distributed prey. 2 Boundary evolution method The particle model (1) or its continuum limit (2) typically produces two relatively well de ned boundaries (see
Discuss the signs of dx/dt and dy/dt in each of those quadrants, and explain what these signs mean for the predator and prey populations. Here is a link for a biological perspective on the Lotka-Volterra model that includes discussion of the four quadrants and the lag of predators behind prey. Predator-Prey Model, University of Tuebingen, Germany.