Stability analysis of traveling wave solutions for lattice reaction-diffusion equations

Cheng Hsiung Hsu, Jian Jhong Lin

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

In this work, we establish a framework to study the stability of traveling wave solutions for some lattice reaction-diffusion equations. The systems arise from epidemic, biological and many other applied models. Applying different kinds of comparison theorems, we show that all solutions of the Cauchy problem for the lattice differential equations converge exponentially to the traveling wave solutions provided that the initial perturbations around the traveling wave solutions belonging to suitable spaces. Our results can be applied to various discrete reaction-diffusion systems, e.g., the discrete multi-species Lotka-Volterra cooperative model, discrete epidemic model, three-species Lotka-Volterra competitive model, etc.

Original languageEnglish
Pages (from-to)1757-1774
Number of pages18
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume25
Issue number5
DOIs
StatePublished - 5 May 2020

Keywords

  • Comparison theorem
  • Lattice reaction-diffusion equations
  • Traveling waves

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