Influence of density-dependent diffusion on pattern formation in a refuge
arXiv:2210.11638 · doi:10.1016/j.physa.2024.130305
Abstract
We investigate a nonlocal generalization of the Fisher-KPP equation, which incorporates logistic growth and diffusion, for a single species population in a viable patch (refuge). In this framework, diffusion plays an homogenizing role, while nonlocal interactions can destabilize the spatially uniform state, leading to the emergence of spontaneous patterns. Notably, even when the uniform state is stable, spatial perturbations, such as the presence of a refuge, can still induce patterns. These phenomena are well known for environments with constant diffusivity. Our goal is to investigate how the formation of winkles in the population distribution is affected when the diffusivity is density-dependent. Then, we explore scenarios in which diffusivity is sensitive to either rarefaction or overcrowding. We find that state-dependent diffusivity affects the shape and stability of the patterns, potentially leading to either explosive growth or fragmentation of the population distribution, depending on how diffusion reacts to changes in density.
9 pages, 8 figures
References in corpus (18)
- Statistical Mechanics of Interacting Run-and-Tumble Bacteria
- Arrested phase separation in reproducing bacteria: a generic route to pattern formation?
- Non-local Interaction Effects on Pattern Formation in Population Dynamics
- Clustering, advection and patterns in a model of population dynamics with neighborhood-dependent rates
- Escape time in anomalous diffusive media
- Applicability of the Fisher Equation to Bacterial Population Dynamics
- On localized vegetation patterns, fairy circles and localized patches in arid landscapes
- Vegetation pattern formation in semiarid systems without facilitative mechanisms
- Dynamics-dependent density distribution in active suspensions
- Nonlinearity in Bacterial Population Dynamics: Proposal for Experiments for the Observation of Abrupt Transitions in Patches
- Motility of \textit{Escherichia coli} in a quasi-two-dimensional porous medium
- Non-extensive random walks
- Nonlinear diffusion effects on biological population spatial patterns
- Critical patch size reduction by heterogeneous diffusion
- Macroscopic description of particle systems with non-local density-dependent diffusivity
- Landscape-induced spatial oscillations in population dynamics
- Interplay between scales in the nonlocal FKPP equation
- Population dynamics in an intermittent refuge