Monotone traveling waves for delayed lotka-volterra competition systems

Jian Fang; Jianhong Wu

doi:10.3934/dcds.2012.32.3043

Monotone traveling waves for delayed lotka-volterra competition systems

Jian Fang^*
, Jianhong Wu

^*Corresponding author for this work

School of Mathematics

York University Toronto

Research output: Contribution to journal › Article › peer-review

32 Scopus citations

Abstract

We consider a delayed reaction-diffusion Lotka-Volterra competi- tion system which does not generate a monotone semi ow with respect to the standard ordering relation for competitive systems. We obtain a necessary and suficient condition for the existence of traveling wave solutions connecting the extinction state to the coexistence state, and prove that such solutions are monotone and unique (up to translation).

Original language	English
Pages (from-to)	3043-3058
Number of pages	16
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	32
Issue number	9
DOIs	https://doi.org/10.3934/dcds.2012.32.3043
State	Published - Sep 2012

Keywords

Delay
Lotka-Volterra competition system
Non-monotone systems
Time lags
Traveling waves

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10.3934/dcds.2012.32.3043

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abstract = "We consider a delayed reaction-diffusion Lotka-Volterra competi- tion system which does not generate a monotone semi ow with respect to the standard ordering relation for competitive systems. We obtain a necessary and suficient condition for the existence of traveling wave solutions connecting the extinction state to the coexistence state, and prove that such solutions are monotone and unique (up to translation).",

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AB - We consider a delayed reaction-diffusion Lotka-Volterra competi- tion system which does not generate a monotone semi ow with respect to the standard ordering relation for competitive systems. We obtain a necessary and suficient condition for the existence of traveling wave solutions connecting the extinction state to the coexistence state, and prove that such solutions are monotone and unique (up to translation).

KW - Delay

KW - Lotka-Volterra competition system

KW - Non-monotone systems

KW - Time lags

KW - Traveling waves

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JO - Discrete and Continuous Dynamical Systems- Series A

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ER -

Monotone traveling waves for delayed lotka-volterra competition systems

Abstract

Keywords

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