Lyapunov functions for a non-linear model of the X-ray bursting of the microquasar GRS 1915+105. (January 2017)

• Record Type: Journal Article
• Authors: Ardito, A.; Ricciardi, P.; Massaro, E.; Mineo, T.; Massa, F.
• Is Part Of: International journal of non-linear mechanics. Volume 88(2017)
• Page Start: 142
• Page End: 147
• Publication Date: 2017-01
• Subjects: Non-linear systems -- Lyapunov function -- Microquasar oscillations; Nonlinear mechanics -- Periodicals; Mécanique non linéaire -- Périodiques; Nonlinear mechanics; Periodicals; 531
• DOI: 10.1016/j.ijnonlinmec.2016.10.017
• Languages: English
• ISSNs: 0020-7462

Abstract

Abstract: 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. Abstract : Highlights: 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.