The effects of diffusion and spatial variation in Lotka–Volterra competition–diffusion system I: Heterogeneity vs. homogeneity
By Xiaoqing He, Wei-Ming Ni. 2013
147 citations recorded by the source corpus.
Abstract It is well known that the interactions between diffusion and spatial heterogeneity could create very interesting phenomena. In this series of two papers, using the classical Lotka–Volterra competition system, we will illustrate the combined effects of dispersal and spatial variations on the outcome of the competition. In Part I, with the total resources being fixed at exactly the same level, we first show that a heterogeneous distribution of resources is usually superior to its homogeneous counterpart in the presence of diffusion. Then we study the more general case when both species have heterogeneous carrying capacities, but still with the same total resources. Limiting behaviors of co-existence steady states as the dispersal rates tend to 0 or ∞ are also obtained. In Part II, we continue our investigation but under much broader situations – including different strengths and distributions of the resources, and with different competition abilities.
Subfields: Genetics, Modeling and Simulation, Public Health, Environmental and Occupational Health
View Paper: https://www.semanticscholar.org/paper/4e551234f87b055a44edb9f9c715f1737d42fcde
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Citations in the corpus
- 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”
- A remark on the global dynamics of competitive systems on ordered Banach spaces (2015, background): “See, for instance, [2] for patch models, [3] for nonlocal operators, and [1, 4, 9, 10] for reaction-diffusion models.”