Asymptotic analysis of the bistable Lotka-Volterra competition-diffusion system

Zihao Wang*, A. Bayliss, V. A. Volpert

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We study traveling wave solutions of the Lotka-Volterra competition-diffusion system for two species with bistable nonlinearity. We analyze the speed of propagation and, most importantly, the sign of the speed, which determines the winner of the competition, in several limiting cases. One we refer to as the strong competition. Here the inter-species competition for each species is much stronger than the intra-species competition. Another is a moderate competition, where the inter- and intra-species competitions are close to each other in strength. We also analyze the cases of fast and slow competitors, i.e., when the diffusion coefficient of one of the species is much larger (or much smaller) than the other. We employ asymptotic and perturbation methods and support our approximate results by direct numerical integration.

Original languageEnglish (US)
Article number127371
JournalApplied Mathematics and Computation
StatePublished - Nov 1 2022


  • Asymptotic analysis
  • Bistable traveling waves
  • Lotka-Volterra competition
  • Perturbative approach
  • Propagation speed

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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