2 research outputs found
An Adaptive Algorithm for Synchronization in Diffusively Coupled Systems
We present an adaptive algorithm that guarantees synchronization in
diffusively coupled systems. We first consider compartmental systems of ODEs,
where each compartment represents a spatial domain of components interconnected
through diffusion terms with like components in different compartments. Each
set of like components may have its own weighted undirected graph describing
the topology of the interconnection between compartments. The link weights are
updated adaptively according to the magnitude of the difference between
neighboring agents connected by the link. We next consider reaction-diffusion
PDEs with Neumann boundary conditions, and derive an analogous algorithm
guaranteeing spatial homogenization of solutions. We provide a numerical
example demonstrating the results