Warning signs for wave speed transitions of noisy Fisher-KPP invasion fronts
arXiv:1212.0356 · doi:10.1007/s12080-013-0189-1
Abstract
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.
14 pages, 8 figures; preprint - comments and suggestions welcome
References in corpus (1)
Cited by in corpus (6)
- Slowly varying control parameters, delayed bifurcations and the stability of spikes in reaction-diffusion systems
- Early-Warning Signs for Pattern-Formation in Stochastic Partial Differential Equations
- A collective coordinate framework to study the dynamics of travelling waves in stochastic partial differential equations
- Numerical Continuation and SPDE Stability for the 2D Cubic-Quintic Allen-Cahn Equation
- Heterogeneous Population Dynamics and Scaling Laws near Epidemic Outbreaks
- Scaling Laws and Warning Signs for Bifurcations of SPDEs