We present the operator semigroups approach to the first- and second-order dynamical systems taking place on metric graphs. We briefly survey the existing results and focus on the well-posedness of the problems with standard vertex conditions. Finally, we show two applications to biological models.
This article is part of the theme issue ‘Semigroup applications everywhere’.
This paper proposes a new method of construction of Lyapunov functionals for the dynamical systems described by fractional differential equations and fractional partial differential equations. The proposed method is rigorously presented. Furthermore, the method is applied to establish the global stability of some fractional biological models with and without diffusion.
Semigroups for dynamical processes on metric graphs