2012/12/03 by Christian Kuehn · 18 citations
Biochemistry, Genetics and Molecular Biology · Environmental Science · Mathematics · Medicine · Physics and Astronomy · Social Sciences · #Acceleration #Applied mathematics #Artificial intelligence #Biology #Classical mechanics #Closeness #Computer science #Control theory (sociology) #Ecology #Economics #Ecosystem dynamics and resilience #Evolutionary Game Theory and Cooperation #Mathematical analysis #Mathematical and Theoretical Epidemiology and Ecology Models #Mathematics #Observer (physics) #Order (exchange) #Physics #Quantum mechanics #Statistical physics #Traveling wave #Work (physics) #math.DS #math.PR #nlin.PS #q-bio.PE
paper · pdf · doi:10.1007/s12080-013-0189-1
published in Theoretical Ecology 6(3), 295-308 (Springer Science+Business Media) · 14 pages, 8 figures; preprint - comments and suggestions welcome
arxiv created 2012/12/03 · openalex publication_date 2013/05/17 · arxiv updated 2015/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Invasion waves are a fundamental building block of theoretical ecology. In this study we aim to take the first steps to link propagation failure and fast acceleration of traveling waves to critical transitions (or tipping points). The approach is based upon a detailed numerical study of various versions of the Fisher-Kolmogorov-Petrovskii-Piscounov (FKPP) equation. The main motivation of this work is to contribute to the following question: how much information do statistics, collected by a stationary observer, contain about the speed and bifurcations of traveling waves? We suggest warning signs based upon closeness to carrying capacity, second-order moments and transients of localized initial invasions.