The equations:

Matlab code

%% #4 % % WRITE CODE BELOW: % Step 1: Write code to solve the system of ODEs given by the Lorenz system % (the equation in 1c) on the interval [0,100] where f(1)=[10;10;10]. Use % ODE45 for this. % Step 2: Use plot3 on each column of your solution vector (f(:,1), f(:,2), % f(:,3)) % Step 3: Label your plot and enjoy some cool looking math! % Step 4: Repeat steps 1-3 with a new intial condition of % f(1)=[100;100;100] % % WRITE A COMMENT BELOW: % Does changing the inital condition from [10;10;10] to something like % (100;100;100] change how your solution Looks? Explain. %% #1 olo 1 1 1 % WRITE CODE BELOW: % Recall how to define anonymous functions from the lecture % a) Define an anonymous function dfl(x,y) -y % b) Define an anonymous function df2(x,y) 2*y/x % c) Define an anonymous function df3(x,y) [10* (y (2)-y (1)); y (1) * (28-y (3))-y (2); y (1) *y (2) -8/3*y (3)] olo olo old %% #4 % % WRITE CODE BELOW: % Step 1: Write code to solve the system of ODEs given by the Lorenz system % (the equation in 1c) on the interval [0,100] where f(1)=[10;10;10]. Use % ODE45 for this. % Step 2: Use plot3 on each column of your solution vector (f(:,1), f(:,2), % f(:,3)) % Step 3: Label your plot and enjoy some cool looking math! % Step 4: Repeat steps 1-3 with a new intial condition of % f(1)=[100;100;100] % % WRITE A COMMENT BELOW: % Does changing the inital condition from [10;10;10] to something like % (100;100;100] change how your solution Looks? Explain. %% #1 olo 1 1 1 % WRITE CODE BELOW: % Recall how to define anonymous functions from the lecture % a) Define an anonymous function dfl(x,y) -y % b) Define an anonymous function df2(x,y) 2*y/x % c) Define an anonymous function df3(x,y) [10* (y (2)-y (1)); y (1) * (28-y (3))-y (2); y (1) *y (2) -8/3*y (3)] olo olo old