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Abstract: We consider a diffusion process on the edges of a finite network and allowfor feedback effects between different, possibly non-adjacent edges. Thisgeneralizes the setting that is common in the literature, where the onlyconsidered interactions take place at the boundary, i. e., in the nodes of thenetwork. We discuss well-posedness of the associated initial value problem aswell as contractivity and positivity properties of its solutions. Finally, wediscuss qualitative properties that can be formulated in terms of invariance oflinear subspaces of the state space, i. e., of symmetries of the associatedphysical system. Applications to a neurobiological model as well as to a systemof linear Schroedinger equations on a quantum graph are discussed.



Author: Stefano Cardanobile, Delio Mugnolo, Robin Nittka

Source: https://arxiv.org/







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