Lyapunov functions for a non-linear model of the X-ray bursting of the microquasar GRS 1915+105

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. •The microquasar GRS 1915+105 exhibits long series of X-ray bursts.•A non-linear ODE system is used to model the shapes of these bursts.•A bi-parametric family of Lyapunov functions is introduced.•Sufficient conditions for the global asymptotic stability are given.•The transition to stable states due to changes of a single parameter is studied.