xt 1 = 2(1 − xt)xt − βxtyt yt 1 = 0.8yt 3βxtyt. 5.5. HIGHER ORDER AND NONLINEAR DISCRETE DYNAMICAL SYSTEMS 73 Here xt and yt represent population densities of the prey and predator populations, respectively. The parameter β represents the conversion rate at which an encounter between the two species results in a decrease in prey and an increase in predators. Suppose that the initial populations are x0 = 0.6, y0 = 0.1, and assume that β = 0.5. Plot the solution curves of the prey and predator population versus time, as well as a trajectory plot of the two populations together. Can the two populations coexist?
