,

where is a dimensionless temperature, depends on the overall heat transfer coefficient, and depends on the activation energy.

The system presents multiple steady states, as you can see from the bifurcation diagram. Plotting the heat losses (shown in magenta) and the heat production term (shown in blue) makes it clear that three steady states (i.e., three intersection points identified by the red dots) can be obtained for some values of and .

The bifurcation diagram is obtained using two different techniques: (1) using the arc length continuation method; and (2) using the Mathematica built-in command ContourPlot.

Perfect agreement is obtained using these two methods. Finally, turning points are shown by the green dots.