FitzHugh-Nagumo model, phase space

FitzHugh-Nagumo (FHN) Model
for one cell (phase space)

This applet shows the membrane potential produced by a cell using the FHN model. The upper plot shows the membrane potential plotted in phase space (state space), where the axes are the two variables u and v. The red curve is the function du/dt=0 and the green line is the function dv/dt=0. Note that the membrane potential closely follows portions of the red curve during the action potential plateau and during rest, while it rapidly jumps from one branch to the other during the action potential upstroke and during repolarization. These curves are called nullclines, and their locations shift depending on the parameter values. The arrows in the plot indicate the direction of the derivative du/dt, with blue arrows indicating positive derivatives and pink arrows negative. Trajectories tend to follow these arrows toward the nullclines.

The lower plot shows the membrane potential as a function of time after it is stimulated above its threshold for excitation in the upper plot.

To use the applet, click in the upper plot. The coordinates of the point selected serve as initial conditions for the simulation.

Things to try:

  • Click in different locations to see the effects of setting different initial conditions.
  • Change the model parameter delta to 0.03 or larger to change the system from excitable to auto-oscillatory.
  • Increase epsilon to decrease the action potential duration and vice versa (try 0.05 and 0.001).
  • Initiatve a sub-threshold stimulus by clicking, for instance, in the region between the green line and the positively-sloped portion of the red curve, and observe that no action potential results.

    The FHN model can be found in
    FitzHugh R. (1961) Biophys J 1, 445-466.
    or more information can be found, for example, in
    Courtemanche M, Skaggs W, Winfree AT. (1990) Physica D 41, 173.