Reaction-diffusion-advection models for the effects and evolution of dispersal
By Chris Cosner. 2013
181 citations recorded by the source corpus.
This review describes reaction-advection-diffusion models for the ecological effects and evolution of dispersal, and mathematical methods for analyzing those models. The topics covered include models for a single species, models for ecological interactions between species, and models for the evolution of dispersal strategies. The models are all set on bounded domains. The mathematical methods include spectral theory, specifically the theory of principal eigenvalues for elliptic operators, maximum principles and comparison theorems, bifurcation theory, and persistence theory.
Subfields: Genetics, Modeling and Simulation, Public Health, Environmental and Occupational Health
View Paper: https://www.semanticscholar.org/paper/40c04280616668342d63f48e1f7b5d10b46aa268
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In Genetics
In Modeling and Simulation
In Public Health, Environmental and Occupational Health
Citations in the corpus
- Qualitative analysis of a Lotka-Volterra competition system with advection (2014, background): “-see [4] and the references therein for more details.”
- Global dynamics and spatio-temporal patterns of predator–prey systems with density-dependent motion (2019, background): “There are three types of basic interspecific interactions (see [8, 15, 24]): predator-prey, competition and mutualism, which can be encapsulated in F(u, v) and G(u, v) by the following typical form: F(u, v) = c1uF (v) + h(u), G(u, v) = f(v)− c2uF (v) (1.”
- Global stability of prey-taxis systems (2017, unknown): “Other type of functional response functions and predator–prey interactions can be found in the excellent surveys [7,24,38].”
- Local dynamics of a diffusive predator–prey model in spatially heterogeneous environment (2017, methodology): “We refer to [7, 23, 24, 25, 26] for surveys of recent development on the effects of dispersal and spatial heterogeneity on population dynamics; See [2, 11, 21, 18] for single species models, [9, 10, 12, 13, 14, 27] for predator-prey models, and [15, 16, 17, 19, 20] for competition models.”