2022/10/02 by B. Geiger, Geiger, Benedikt
Computer Science · Physics and Astronomy · #35E20 #35L40 (Primary) #47A10 (Secondary) #47D06 #92C15 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Biological sciences #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Quantitative Methods (q-bio.QM) #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2210.00416
openalex publication_date 2022/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study general linear transport-reaction systems on an arbitrary dimensional hypercube with periodic boundary conditions. Transport-reaction systems are often used to model the finite speed movement and interaction of particles, bacteria or animals. We first show a weak spectral mapping theorem and demonstrate its' application. Secondly, we introduce a certain class of so-called hyperbolic instabilities, which provide a natural framework for transport-driven instabilities on one-dimensional domains: They are either Turing patterns or increasingly oscillating hyperbolic instabilities. A new algebraic condition for the existence of Turing patterns is obtained as a side-product.