math modeling problem

R programming exercise: 4. Consider another variation of the competition model, in which both populations experience logistic growth in the absence of the other population. You will perform a graphical analysis in R for this model, given by the following system: = aW(K1 W) bWL d dt dL dt cL(K2 L) - DWL. == = (a) How many equilibrium values does this system have? One of the equilibria represents coexis- tence of the two species you do not need to find the exact values for this equilibrium, but find all of the other equilibrium values. (b) Using the parameter values a = 0.2,b = 0.1,c = 0.3, d 0.1, K1 = 2, K2 2.5, plot a slope field of this system, with nullclines, in R. (c) Add a sample set of trajectories to the phase portrait plot from (b). Include this plot in your homework submission. (d) Based on your phase portrait, what is the stability each equilibrium value? (e) For one of the trajectories on your phase portrait (i.e. one set of initial conditions), graph the solution curves, W vs. t and L vs. t, on the same plot. Include this plot in your homework submission. R programming exercise: 4. Consider another variation of the competition model, in which both populations experience logistic growth in the absence of the other population. You will perform a graphical analysis in R for this model, given by the following system: = aW(K1 W) bWL d dt dL dt cL(K2 L) - DWL. == = (a) How many equilibrium values does this system have? One of the equilibria represents coexis- tence of the two species you do not need to find the exact values for this equilibrium, but find all of the other equilibrium values. (b) Using the parameter values a = 0.2,b = 0.1,c = 0.3, d 0.1, K1 = 2, K2 2.5, plot a slope field of this system, with nullclines, in R. (c) Add a sample set of trajectories to the phase portrait plot from (b). Include this plot in your homework submission. (d) Based on your phase portrait, what is the stability each equilibrium value? (e) For one of the trajectories on your phase portrait (i.e. one set of initial conditions), graph the solution curves, W vs. t and L vs. t, on the same plot. Include this plot in your homework submission