Example model 1 ODE modeling with Berkeley Madonna：1例模型建模与麦当娜颂伯克利.doc

Software URLs: / Follow the online tutorial http://www.pathogenomics.ca/cerebral/ Follow the online tutorial http://innatedb.ca/ Follow the tutorials under Help /IIDB Follow the online tutorial /quickStart/QuickStart.html Follow this link for tutorial / Try the models below /software/Dizzy/ Try the models below . 1: ODE modeling with Berkeley Madonna Install and run the freely available Berkeley Madonna (BM) software from /download.html , then copy the model below. You can download the Berkeley Madonna manual separately from /BM%20Users%20Guide%208.0.pdf When you first invoke Berkeley Madonna, it comes up with a registration dialog box. If you don’t want to purchase the full version, simply click cancel, then click FILE NEW to open a new model file. In Berkeley Madonna, comment lines start with a semi-colon (;) and the prime symbol (’) can be used to denote the derivative of a variable (e.g. C’ is the same as dC/dt). In the free version of BM, you cannot save model files. But you can save your equations as plain text files (i.e. with extension ‘.txt’), which BM can read. Below is the Berkeley Madonna model description file for an athlete accelerating at the start of a race. The athlete’s acceleration is defined as the second derivative of her position (position”). position’ gives her speed. Plot the athlete’s position, speed and acceleration over time and verify that the area under the acceleration curve gives the speed and the area under the speed curve gives the position. METHOD RK4 STARTTIME = 0 STOPTIME = 25 DT = 0.01 acceleration = 0.3 init position = 0 init position = 0 position = acceleration The first line of the file specifies the numerical integration method (BM has several). The next three lines specify the simulation settings. DT is the step size for the numerical integrator (how often the ODE is evaluated). The model description starts by defining the parameters and initial conditions (i.e. at time z