Global asymptotic stability in a model of networks. Issue 1 (2nd January 2018)

• Record Type: Journal Article
• Authors: Fathallah-Shaykh, Hassan M.; Freiji, Abraham
• Is Part Of: Dynamical systems. Volume 33:Issue 1(2018)
• Page Start: 159
• Page End: 183
• Publication Date: 2018-01-02
• Subjects: Global asymptotic stability -- Lyapunov function -- Lyapunov diagonal stability -- networks -- dynamics; 34.D23; Differentiable dynamical systems -- Periodicals; 515.35205
• DOI: 10.1080/14689367.2017.1326464
• Languages: English
• ISSNs: 1468-9367

Abstract

ABSTRACT: Global asymptotic stability is of importance from a theoretical as well as an application point of view in several fields. We study a system of cubic polynomials that models biological networks. We classify the equilibria and show that the property that the interconnection matrix is Lyapunov diagonally stable is a key feature that determines convergence to a single equilibrium. The results are applied to chains of negative edges, cycles, and to interconnected graphs. We give numerical examples and study network graphs obtained from a model of the Drosophila circadian clock.