Stability Of Reaction-diffusion Systems Research Articles

Reaction-Diffusion Systems in the Port-Hamiltonian Framework

Reaction-diffusion systems model the evolution of the constituents distributed in space under the influence of chemical reactions and diffusion. These systems arise naturally in chemistry, but can also be used to model dynamical processes beyond the realm of chemistry such as in biology, ecology, geology, and physics. In this paper, by adopting the viewpoint of port-based modeling, we cast reaction-diffusion systems into the port-Hamiltonian framework. Aside from offering conceptually a clear geometric interpretation formalized by a Stokes-Dirac structure, a port-Hamiltonian perspective allows to treat these dissipative systems as interconnected and thus makes their analysis, both quantitative and qualitative, more accessible from a modern dynamical systems and control theory point of view. This modeling approach permits us to draw immediately some conclusions regarding passivity and stability of reaction-diffusion systems. Furthermore, by adopting a discrete differential geometry-based approach and discretizing the reaction-diffusion system in the port-Hamiltonian form, apart from preserving a geometric structure, a compartmental model analogous to the standard one is obtained.