  The low-temperature-differential (LTD) Stirling heat engine technology
constitutes one of the important sustainable energy technologies. The basic
question of how the rotational motion of the LTD Stirling heat engine is
maintained or lost based on the temperature difference is thus a practically
and physically important problem that needs to be clearly understood. Here, we
approach this problem by proposing and investigating a minimal nonlinear
dynamic model of an LTD kinematic Stirling heat engine. Our model is described
as a driven nonlinear pendulum where the motive force is the temperature
difference. The rotational state and the stationary state of the engine are
described as a stable limit cycle and a stable fixed point of the dynamical
equations, respectively. These two states coexist under a sufficient
temperature difference, whereas the stable limit cycle does not exist under a
temperature difference that is too small. Using a nonlinear bifurcation
analysis, we show that the disappearance of the stable limit cycle occurs via a
homoclinic bifurcation, with the temperature difference being the bifurcation
parameter.
