Global asymptotic stability in a model of networks

Academic Article

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.
  • Digital Object Identifier (doi)

    Author List

  • Fathallah-Shaykh HM; Freiji A
  • Start Page

  • 159
  • End Page

  • 183
  • Volume

  • 33
  • Issue

  • 1