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Instructions for setting up Software for ODEs using Matlab
(this is the software used to prepare most of the graphics in the course handouts)	(1)  Download the software:  You need to download two Matlab files called dfield6.m and pplane6.m to a directory of your choosing in your file space. You could download the files to the directory U:\maths\matlab and this probably means that the path is automatically included, in which case you need not do (2) below.  I have not tested this.  You go ahead and test it and tell me how it goes. (2)  Tell Matlab where to find the files:  you need to type addpath X:\my_home\chosen_dir; ... on the Matlab command line, where you have to indicate the right path to where you have downloaded the .m files.  The letter X used here represents the drive, and you need to check what letter is used for the mapped drive where your file space is, and use that instead of X.  If the path contains directory names with spaces in them, then you need to enclose the whole path in single quotes in the command above.  For further help from Matlab, type help addpath ... on the Matlab command line. You have to add paths to Matlab after starting each session.  If you want to avoid doing this, you can add the line addpath X:\my_home\chosen_dir; ... as above, to a file called startup.m, which is for users to put their own startup commands.  Then you never have to worry about adding this path again. (3) Once the above is done, you are ready to use the sofware.  All you need to do is, at the Matlab prompt, type pplane6 ... and a GUI will open where you can start inputting your autonomous system to study. If you encounter problems: - Ask for support by emailing support-maths@bristol.ac.uk - Go see one of the computer officers - You can email me (the lecturer), but I may not be able to help (I don't know the workings of the UG labs). TIPS on using the software After you input the differential equations, click Proceed to see the direction field. You can plot several trajectories by clicking on the initial condition (any point in the phase plane).  The trajectory is plotted backwards and forwards in time. You can visually identify where the equilibrium points might be, then click the Menu item Solutions>Find an equilibrium point ... and click near to where you think it might be.  The software finds it, and opens a dialog box giving you the Jacobian, the eigenvalues and the eigenvectors. You can click a button there to see the linearization (a local phase portrait of the linearized system). You can also plot the nullclines and many other things.  Explore the software yourself. You can edit the appearance of the graph by clicking the Menu item Edit>Current Object Propertites... ... then choose the object (e.g., line) and change color, thickness, etc. You can save the plot as an .eps or .jpg, but remember first to do this: click on File>Page Setup... ... then click the tab "Axes and Figure", and uncheck "Print UI Controls". Then go to File>Save As... ... and choose a file name and extension.
	Created:  30 Nov. 2004