# American Institute of Mathematical Sciences

November  2012, 17(8): 2653-2669. doi: 10.3934/dcdsb.2012.17.2653

## Exact travelling wave solutions of three-species competition--diffusion systems

 1 Department of Mathematics, National Taiwan University, and National Center for Theoretical Sciences (Taipei Office), No. 1, Sec. 4, Roosevelt Road, Taipei, 10617, Taiwan 2 Department of Mathematics, National Taiwan University, and National Center for Theoretical Sciences (Taipei Office), No. 1, Sec. 4, Roosevelt Road, Taipei, 10617, Taiwan 3 Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, 1-1-1 Higashimita, Tamaku, Kawasaki 214-8571, Japan 4 Meiji Institute for Advanced Study of Mathematical Sciences, and Graduate School of Advanced Mathematical Sciences, Meiji University, 1-1-1 Higashimita, Tamaku, Kawasaki 214-8571, Japan

Received  March 2011 Revised  September 2011 Published  July 2012

We consider the problem where $W$ invades the $(U,V)$ system in the three species Lotka-Volterra competition-diffusion model. Numerical simulation indicates that the presence of $W$ can dramatically change the competitive interaction between $U$ and $V$ in some parameter range if the invading $W$ is not too small. We also construct exact travelling wave solutions with non-trivial three components and track the bifurcation branches of these solutions by AUTO.
Citation: Chiun-Chuan Chen, Li-Chang Hung, Masayasu Mimura, Daishin Ueyama. Exact travelling wave solutions of three-species competition--diffusion systems. Discrete & Continuous Dynamical Systems - B, 2012, 17 (8) : 2653-2669. doi: 10.3934/dcdsb.2012.17.2653
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##### References:
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