Exercise 8.4.3 Verify that the steady states (0,0) and (2,0) are saddles, and that (1,0.5) is a stable spiral. Note that if you also are interested in eigenvectors for each eigenvalue, then you can type, for example 28 >>[V,e]-eig(m3) This will give you two matrices. The columns of the first matrix correspond to the eigenvectors, and the entries of the second matrix correspond to the eigenvalues. We can go further and visualize the phase portrait. For this, we first need to solve the system of differential equations. Since an explicit solution cannot be found, we will again need to rely on one of Matlab's ode solvers. In an m-file type: function dwodefun3 (t,w) k#2 Save your m-file. Now, in the command window type: >> [t,w1] ode45('odefun3', [0,100],[2,0.8]) >>[t,u2] ode45('odefun3', [0,100], [0.5,0.8]) We now graph the phase portrait defined by the above differential equations corresponding to the two different initial conditions described above Exercise 8.4.3 Verify that the steady states (0,0) and (2,0) are saddles, and that (1,0.5) is a stable spiral. Note that if you also are interested in eigenvectors for each eigenvalue, then you can type, for example 28 >>[V,e]-eig(m3) This will give you two matrices. The columns of the first matrix correspond to the eigenvectors, and the entries of the second matrix correspond to the eigenvalues. We can go further and visualize the phase portrait. For this, we first need to solve the system of differential equations. Since an explicit solution cannot be found, we will again need to rely on one of Matlab's ode solvers. In an m-file type: function dwodefun3 (t,w) k#2 Save your m-file. Now, in the command window type: >> [t,w1] ode45('odefun3', [0,100],[2,0.8]) >>[t,u2] ode45('odefun3', [0,100], [0.5,0.8]) We now graph the phase portrait defined by the above differential equations corresponding to the two different initial conditions described above