Traveling Waves in Discrete Periodic Media for Bistable Dynamics |
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Authors: | Xinfu Chen Jong-Shenq Guo Chin-Chin Wu |
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Institution: | (1) Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA;(2) Department of Mathematics, National Taiwan Normal University, Taipei, 11677, Taiwan;(3) Department of Mathematics, National Taiwan Normal University, Taipei, 11677, Taiwan |
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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. |
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Keywords: | |
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