To run the analyses from Section 3 and generate Figures 2a, 3a, and 4a, follow the steps below.
- Download and install MatCont following the instructions from the MatCont developers.
- In the main MatCont folder, find the subfolder Systems. Place the contents of the Systems folder from this repo into that folder as well.
- Open Matlab and run MatCont
- Choose Select > System > Load/Edit/Delete Systems.
- Select larter-breakspear from the list on the left and click the Load button.
- In the Main window, select Type > Initial Point > Point.
- This should load the variables into the Integrator and Starter windows. Check to make sure the parameters all match Table 1 (and t=0, V and Z are in (-1, 1), and W is in (0, 1)).
- To observe the parameters changing, in the main window select Window/Output > Numeric (launches Numeric window) and Window/Output > Graphic > 3D plot.
- Select Compute > Forward. This will produce a graph of the standard oscillations in 3D.
- Once this has run, select Type > Initial Point > Equilibrium.
- In the Starter window, you need to select the ion you’re interested in continuing (V_Na, V_K, or V_Ca).
- In the Main window, select Compute > Forward (may need to do Compute > Backward as well depending on your initial conditions).
- Find the Hopf point (the Control window will pause, and you can click Stop).
- Double click on the Hopf point in the Graphic window and say Yes to the prompt to load it.
- In the Main window, select Compute > Forward and you’ll generate the results for the figure. Whenever it pauses at a point, note the values in the Numeric window.