Consider the system dx dt = (x)(1 ?y)?xy, dy dt = ?5xy +(4y)(1? y 4 ), where x and y denote the sizes of two interacting populations. (1.1) (1.2) (1.3) How does the x species and the y species, respectively, behave in the absence of the other species? Describe the type of interaction between the two species (e.g. competition, predator-prey, etc.). Draw the phase diagram (note that phase diagrams drawn by an automated plotter will be awarded zero) and use it to predict the outcome of the system if initially x0 = 1, y0 = 1.