Single spreading speed and traveling wave solutions of a diffusive pioneer-climax model without cooperative property

Jiamin Cao; Peixuan Weng

doi:10.3934/cpaa.2017067

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2017, Volume 16, Issue 4: 1405-1426. Doi: 10.3934/cpaa.2017067

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Single spreading speed and traveling wave solutions of a diffusive pioneer-climax model without cooperative property

Jiamin Cao and
Peixuan Weng^,

South China Normal University, Guangzhou, China

^* Corresponding author: P. X. Weng
^* Corresponding author: P. X. Weng

Received: July 2015

Revised: August 2016

Published online: July 2017

Research is supported by the Natural Science Foundation of China (11171120), and the The Natural Science Foundation of Guangdong Province (2016A030313426).

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Abstract

A diffusive competing pioneer and climax system without cooperative property is investigated. We consider a special case in which the system has no co-existence equilibrium. Under the appropriate assumptions, we show the linear determinacy and the existence of single spreading speed. Furthermore, we obtain the existence of traveling wave solution which connects two boundary equilibria, and also confirm that the spreading speed coincides with the minimal wave speed. The results in this article reveals a phenomenon of strongly biological invasion which implies that the invasion of a new species will leads to the extinction of the resident species.

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Mathematics Subject Classification: Primary: 35K57, 92D25.

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Figure 1. Equilibria of system (4) under (A1) or (A2)

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