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Volume 21, Issue 4
Estimation for the Asymptotic Behavior of the Delayed Competition Model

Huifeng Li & Jinliang Wang

J. Part. Diff. Eq., 21 (2008), pp. 289-302.

Published online: 2008-11

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  • Abstract

In ecological dynamic systems, the competition between species is a very universal phenomenon, which can be described by the well-known Volterra-Lotka model in a diffusion form. Noticing that the living space usually changes in a seasonal manner and the population development of the species may also undergo time-delay impact, a developed form of this model is investigated in this article. The main approaches employed here are the upper-lower solution method and the energy-estimate technique. The results show that whether the species may sustain survival or not depends on the relations among the birth rate, the death rate, the competition rate, the diffusivity and the time delay. For the survival case, the population evolutions of the two species may appear asymptotic periodicity with distinct upper bound and this bound depends heavily on the time delay. These results can be also checked by the intuitionistic numerical simulations.

  • Keywords

Volterra-Lotka diffusion periodic asymptotic time delay

  • AMS Subject Headings

35B10 35B40 35K55.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

wangjinliang10@sina.com.cn (Jinliang Wang)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-21-289, author = {Li , Huifeng and Wang , Jinliang}, title = {Estimation for the Asymptotic Behavior of the Delayed Competition Model}, journal = {Journal of Partial Differential Equations}, year = {2008}, volume = {21}, number = {4}, pages = {289--302}, abstract = {

In ecological dynamic systems, the competition between species is a very universal phenomenon, which can be described by the well-known Volterra-Lotka model in a diffusion form. Noticing that the living space usually changes in a seasonal manner and the population development of the species may also undergo time-delay impact, a developed form of this model is investigated in this article. The main approaches employed here are the upper-lower solution method and the energy-estimate technique. The results show that whether the species may sustain survival or not depends on the relations among the birth rate, the death rate, the competition rate, the diffusivity and the time delay. For the survival case, the population evolutions of the two species may appear asymptotic periodicity with distinct upper bound and this bound depends heavily on the time delay. These results can be also checked by the intuitionistic numerical simulations.

}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5283.html} }
TY - JOUR T1 - Estimation for the Asymptotic Behavior of the Delayed Competition Model AU - Li , Huifeng AU - Wang , Jinliang JO - Journal of Partial Differential Equations VL - 4 SP - 289 EP - 302 PY - 2008 DA - 2008/11 SN - 21 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5283.html KW - Volterra-Lotka KW - diffusion KW - periodic KW - asymptotic KW - time delay AB -

In ecological dynamic systems, the competition between species is a very universal phenomenon, which can be described by the well-known Volterra-Lotka model in a diffusion form. Noticing that the living space usually changes in a seasonal manner and the population development of the species may also undergo time-delay impact, a developed form of this model is investigated in this article. The main approaches employed here are the upper-lower solution method and the energy-estimate technique. The results show that whether the species may sustain survival or not depends on the relations among the birth rate, the death rate, the competition rate, the diffusivity and the time delay. For the survival case, the population evolutions of the two species may appear asymptotic periodicity with distinct upper bound and this bound depends heavily on the time delay. These results can be also checked by the intuitionistic numerical simulations.

Li , Huifeng and Wang , Jinliang. (2008). Estimation for the Asymptotic Behavior of the Delayed Competition Model. Journal of Partial Differential Equations. 21 (4). 289-302. doi:
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