Semi-exact solutions and pulsating fronts for Lotka-Volterra systems of two competing species in spatially periodic habitats

Chiun Chuan Chen, Yin Liang Huang, Li Chang Hung*, Chang-Hong Wu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We are concerned with the coexistence states of the diffusive Lotka-Volterra system of two competing species when the growth rates of the two species depend periodically on the spacial variable. For the one-dimensional problem, we employ the generalized Jacobi elliptic function method to find semi-exact solutions under certain conditions on the parameters. In addition, we use the sine function to construct a pair of upper and lower solutions and obtain a solution of the above-mentioned system. Next, we provide a sufficient condition for the existence of pulsating fronts connecting two semi-trivial states by applying the abstract theory regarding monotone semiflows. Some numerical simulations are also included.

Original languageEnglish
Pages (from-to)1-18
Number of pages18
JournalCommunications on Pure and Applied Analysis
Volume19
Issue number1
DOIs
StatePublished - Jan 2020

Keywords

  • Reaction-diffusion equations
  • Semi-exact solutions
  • Traveling wave solutions

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