Some Challenging Mathematical Problems in Evolution of Dispersal and Population Dynamics

By Yuan Lou. 2008

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Global dynamics of a Lotka–Volterra competition–diffusion–advection system in heterogeneous environments (2019, unknown): “In the past few decades, reaction-diffusion equations have been frequently utilized as standard models to address problems related to spatial ecology and evolution, and one of the most successful examples is the two-species Lotka-Volterra competitiondiffusion system; see for instance [12, 13, 15, 16”
The spreading front of invasive species in favorable habitat or unfavorable habitat (2013, background): “To describe the feature of environment, as in [1, 20], we say that r is a favorable site if the local birth rate b(r) is greater than the local death rate d(r).”
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.”
Hopf bifurcation in a delayed reaction-diffusion-advection population model (2017, background): “1) Actually, it follows from [1, 30] that, for τ = 0, model (1.”