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

摘要

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