A maximum principle for diffusive Lotka-Volterra systems of two competing species
Li-Chang Hung, Chiun-Chuan Chen
TL;DR
This paper introduces a maximum principle for two-species diffusive Lotka-Volterra systems, which helps determine the nonexistence of traveling wave solutions in three-species competition models.
Contribution
It presents a novel maximum principle approach for two-species systems and applies it to rule out traveling waves in three-species models.
Findings
Maximum principle established for two-species systems
Nonexistence of traveling waves in three-species systems under certain conditions
New analytical approach for competitive ecological models
Abstract
Using a new approach, we establish a maximum principle for diffusive Lotka-Volterra systems of two competing species. Under certain conditions we show this maximum principle leads to the nonexistence of traveling waves solutions for systems of three competing species.
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Taxonomy
TopicsMathematical and Theoretical Epidemiology and Ecology Models · Advanced Differential Equations and Dynamical Systems