Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Monotonicity and uniqueness of wave profiles for a three components lattice dynamical system

Pages: 2813 - 2827, Volume 37, Issue 5, May 2017      doi:10.3934/dcds.2017121

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Chin-Chin Wu - Department of Applied Mathematics, National Chung Hsing University, 145, Xingda Road, South Dist, Taichung 402, Taiwan (email)

Abstract: We consider a three components lattice dynamical system which arises in the study of a three species competition model. It is assumed that two weaker species have different preferences of food and the third stronger competitor has both preferences of food. Under this assumption, it is well-known that there is the minimal speed such that a traveling wave solution exists for any speed above this minimal one. In this paper, we prove the monotonicity of wave profiles and the uniqueness (up to translations) of wave profiles for each given admissible speed under certain restrictions on parameters.

Keywords:  Lattice dynamical system, traveling wave, wave profile, competition model.
Mathematics Subject Classification:  Primary: 34K05, 34A34; Secondary: 34K60, 34E05.

Received: May 2016;      Revised: December 2016;      Available Online: February 2017.