  This paper introduces a biparametric family of Lyapunov functions for a
non-linear mathematical model based on the FitzHugh-Nagumo equations able to
reproduce some main features of the X-ray bursting behaviour exhibited by the
microquasar GRS 1915+105. These functions are useful to investigate the
properties of equilibrium points and allow us to demonstrate a theorem on the
global stability. The transition between bursting and stable behaviour is also
analyzed.
