Article

Archive for Rational Mechanics and Analysis

, Volume 189, Issue 2, pp 189-236

First online:

Traveling Waves in Discrete Periodic Media for Bistable Dynamics

  • Xinfu ChenAffiliated withDepartment of Mathematics, University of Pittsburgh
  • , Jong-Shenq GuoAffiliated withDepartment of Mathematics, National Taiwan Normal University Email author 
  • , Chin-Chin WuAffiliated withDepartment of Mathematics, National Taiwan Normal University

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Abstract

This paper is concerned with the existence, uniqueness, and global stability of traveling waves in discrete periodic media for a system of ordinary differential equations exhibiting bistable dynamics. The main tools used to prove the uniqueness and asymptotic stability of traveling waves are the comparison principle, spectrum analysis, and constructions of super/subsolutions. To prove the existence of traveling waves, the system is converted to an integral equation which is common in the study of monostable dynamics but quite rare in the study of bistable dynamics. The main purpose of this paper is to introduce a general framework for the study of traveling waves in discrete periodic media.