Consider the system x'(t) = ax - bxy y'(t) = cxy - dy This is known as the Lotka-Volterra predator-prey model for two populations with x(t) being the number of prey and y(t) the number of predators at time t. Let a = 4, b = 2, c = 1, d = 3 and solve the model for 0 lessthanorequalto t lessthanorequalto 5. The initial values are x(0) = 3, y(0) = 5. Plot x and y as functions of t and plot x versus y. Solve the same model with x(0) = 3 and, in succession, y(0) = .5, 1, 1.5, 2. Plot x versus y in each case? What do you observe? Why would the point (3, 2) be an equilibrium point? To solve the above system you are to use the fourth order Adams-Bashforth Adams-Moulton Predictor corrector method using the fourth order Runge-Kutta to start the method. Use a time step of .005. Consider the system x'(t) = ax - bxy y'(t) = cxy - dy This is known as the Lotka-Volterra predator-prey model for two populations with x(t) being the number of prey and y(t) the number of predators at time t. Let a = 4, b = 2, c = 1, d = 3 and solve the model for 0 lessthanorequalto t lessthanorequalto 5. The initial values are x(0) = 3, y(0) = 5. Plot x and y as functions of t and plot x versus y. Solve the same model with x(0) = 3 and, in succession, y(0) = .5, 1, 1.5, 2. Plot x versus y in each case? What do you observe? Why would the point (3, 2) be an equilibrium point? To solve the above system you are to use the fourth order Adams-Bashforth Adams-Moulton Predictor corrector method using the fourth order Runge-Kutta to start the method. Use a time step of .005