Traveling wave solutions for Lotka-Volterra system re-visited | Zendy

Anthony W. Leung | Zendy; Xiaojie Hou | Zendy; Wei Feng | Zendy

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Traveling wave solutions for Lotka-Volterra system re-visited

Author(s) -

Anthony W. Leung,

Xiaojie Hou,

Wei Feng

Publication year - 2010

Publication title -

discrete and continuous dynamical systems - b

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.864

H-Index - 53

eISSN - 1553-524X

pISSN - 1531-3492

DOI - 10.3934/dcdsb.2011.15.171

Subject(s) - monotone polygon , traveling wave , wave speed , mathematics , operator (biology) , exponential growth , mathematical analysis , critical speed , exponential stability , wavenumber , stability (learning theory) , banach space , physics , computer science , nonlinear system , quantum mechanics , geometry , biochemistry , chemistry , repressor , machine learning , transcription factor , gene , vibration

Using a new method of monotone iteration of a pair of smooth lower- and upper-solutions, the traveling wave solutions of the classical Lotka-Volterra system are shown to exist for a family of wave speeds. Such constructed upper and lower solution pair enables us to derive the explicit value of the minimal (critical) wave speed as well as the asymptotic decay/growth rates of the wave solutions at infinities. Furthermore, the traveling wave corresponding to each wave speed is unique up to a translation of the origin. The stability of the traveling wave solutions with non-critical wave speed is also studied by spectral analysis of a linearized operator in exponentially weighted Banach spaces.

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