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We present an adaptive algorithm that guarantees synchronization indiffusively coupled systems. We first consider compartmental systems of ODEs,where each compartment represents a spatial domain of components interconnectedthrough diffusion terms with like components in different compartments. Eachset of like components may have its own weighted undirected graph describingthe topology of the interconnection between compartments. The link weights areupdated adaptively according to the magnitude of the difference betweenneighboring agents connected by the link. We next consider reaction-diffusionPDEs with Neumann boundary conditions, and derive an analogous algorithmguaranteeing spatial homogenization of solutions. We provide a numericalexample demonstrating the results.

An Adaptive Algorithm for Synchronization in Diffusively Coupled Systems