2025/12/08 by Avery, Montie, Holzer, Matt, Scheel, Arnd
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Analysis of PDEs (math.AP) #Diffusion and Search Dynamics #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Gene Regulatory Network Analysis #Pattern Formation and Solitons (nlin.PS) #stochastic dynamics and bifurcation
paper · doi:10.48550/arxiv.2512.07764
openalex publication_date 2025/12/08 · openalex created_date 2025/12/10 · openalex updated_date 2026/07/28
We review progress on questions related to front propagation into unstable states and point out open problems in the area. We strive to highlight different theoretical perspectives and challenges while also addressing more practical questions with examples and guides to computational methods. Throughout we take a dynamical systems point of view that focuses on the ability of invasion processes to act as a selection mechanism in complex systems.