Consider the Lotka-Voterra equations of interacting predator and prey systems[br][center][i]x[/i]'=[i]x[/i]([i]a[/i]-c[i]x[/i]-d[i]y[/i])[br][i]y[/i]'=-[i]y[/i]([i]b[/i]-e[i]x[/i])-[i]h[/i][/center][size=100][size=150]where all of [i]x[/i], [i]y[/i], [i]a[/i], [i]b[/i], [i]c[/i], [i]d[/i], [i]k[/i], [i]n [/i] are positive, and[/size][/size][list][*][i]x[/i] represents the number of prey[/*][*][i]y[/i] represents the number of predators[/*][*][i]a[/i] is the growth rate of the prey.[/*][*][i]b[/i] is the death rate of the predators independent of the prey.[/*][*][i]d[/i] is the is the rate of consumption of the prey per predator.[/*][*][i]a[/i] / c is the carrying capacity of the prey independent of the predators.[/*][*][i]e[/i] is the growth rate of the predator per prey consumed,[/*][*][i]h[/i] is prey harvesting.[/*][/list]This equations include the effect of limited resources on the food supply of the prey, and how the prey are culled or harvested. The following simulation demonstrates the solutions to these equations for a=1, b=0.25, c=0.01, d=0.02 and e=0.02.[br][br]Change the initial conditions and the harvesting to analyse the behaviour of the populations.