Mathematical Models for Interacting Dynamics on Networks

This volume provides a broad overview of state-of-the-art research on dynamical systems on networks. The chapters are based on contributions to the Final Conference of the COST Action 'CA18232: Mat-Dyn-Net: Mathematical Models for Interacting Dynamics on Networks. Specific topics covered include:

• Spectral theory, and mathematical physics
• Kinetic and transport equations
• Biological and biomedical models
• Differential operators and differential equations

Mathematical Models for Interacting Dynamics on Networks will appeal to researchers interested in these active areas.

A review of a work by L. Raymond: Sturmian Hamiltonians with a large coupling constant - periodic approximations and gap labels. - Compactness of linearized Boltzmann operators for polyatomic gases. - Discrete Boltzmann Equation for Anyons. - Action potential dynamics on heterogenous neural networks: from kinetic to macroscopic equations. - A space-dependent Boltzmann-BGK model for gas mixtures and its hydrodynamic limits. - A delayed model for tumor-immune system interactions. - Geometric optimization problem for vascular stents. - Journey Through the World of Dynamical Systems on Networks. - A Payne-Whitham model of urban traffic networks in the presence of traffic lights and its application to traffic optimisation. - A Novel Use of Pseudospectra in Mathematical Biology: Understanding HPA Axis Sensitivity. - The virial theorem and the method of multipliers in spectral theory. - Well-posedness and long-term behaviour of buffered flows in infinite networks. - Numerical Study of the Higher-Order Maxwell-Stefan Model of Diffusion. - Fourth-order operators with unbounded coefficients in $L^1$ spaces. - Graph structure of the nodal set and bounds on the number of critical points of eigenfunctions on Riemannian manifolds. - Investigating dynamics and asymptotic trend to equilibrium in a reactive BGK model. - Polynomial Stability of a Coupled Wave-Heat Network.