MATLAB

Tool Development Consider the species competition problem NI '[t] = r N1 [t] (1 -N1 [t]/K)-a *N1 [t]*N2[t], This set of equations has 9 parameters (r, K, a, s, L, b, N1(0), N2(0),tend) a) Write a function that defines the equations. This function will have the first 8 parameters above in an argument list. b) Create a function serves a main program (that calls the function created in a). This program will create a parametric plot of N1 (t) vs N2(t) for a set of parameters (r, K, a, s, L, b, N1(0), N2(0),tend). Show that this works. In this program create three plots N1(t) vs. t, . . N2(t) vs. t and . N1(t) vs N2(t) (parametric plot) superimposed with two isoclines c) Show that your program in b) works for one set of parameters. Plot the solutions d) Create a new program that expands on the program developed in b). This tool will create only a set of parametric plots using three different values each for (N1 (0), N2(0)) using the same values of (r, K, a, s, L, b). There will be nine different curves on this parametric plot plus the two isoclines. System Analysis Create parametric plots for Cases 1-4 to demonstrate the behavior we have explored graphically. I suggest the following parameter values: Case 1: L>r/, s/B > K r=1 , s-2, =5, =1,K=.5, L=1 Case 2: L K r: 10, s-10, -5, =10, K-5, L=1 . For each case, describe the results, and explain any discrepancies that exist between the predicted behavior and that observed in the simulations. Tool Development Consider the species competition problem NI '[t] = r N1 [t] (1 -N1 [t]/K)-a *N1 [t]*N2[t], This set of equations has 9 parameters (r, K, a, s, L, b, N1(0), N2(0),tend) a) Write a function that defines the equations. This function will have the first 8 parameters above in an argument list. b) Create a function serves a main program (that calls the function created in a). This program will create a parametric plot of N1 (t) vs N2(t) for a set of parameters (r, K, a, s, L, b, N1(0), N2(0),tend). Show that this works. In this program create three plots N1(t) vs. t, . . N2(t) vs. t and . N1(t) vs N2(t) (parametric plot) superimposed with two isoclines c) Show that your program in b) works for one set of parameters. Plot the solutions d) Create a new program that expands on the program developed in b). This tool will create only a set of parametric plots using three different values each for (N1 (0), N2(0)) using the same values of (r, K, a, s, L, b). There will be nine different curves on this parametric plot plus the two isoclines. System Analysis Create parametric plots for Cases 1-4 to demonstrate the behavior we have explored graphically. I suggest the following parameter values: Case 1: L>r/, s/B > K r=1 , s-2, =5, =1,K=.5, L=1 Case 2: L K r: 10, s-10, -5, =10, K-5, L=1 . For each case, describe the results, and explain any discrepancies that exist between the predicted behavior and that observed in the simulations