Abstract
We propose a reaction-diffusion system with nonlocal delays to model the growth of plankton communities feeding on a limiting nutrient supplied at a constant rate. Two delays are incorporated into the model: one describes the delayed nutrient recycling process and the other models the delayed growth response of the plankton. It is assumed that both delays are nonlocal in the sense that there are delayed not only in time but also in space. Local and bifurcation analyses are carried out. It has been shown that Turing-type spatial patterns occur when the diffusion coefficients vary and temporal or spatial-temporal patterns occur when the delay involved in the growth response changes.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 269-286 |
| Number of pages | 18 |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 258 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jun 1 2001 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Analysis
- Applied Mathematics
Cite this
Instability in diffusive ecological models with nonlocal delay effects. / Boushaba, Khalid; Ruan, Shigui.
In: Journal of Mathematical Analysis and Applications, Vol. 258, No. 1, 01.06.2001, p. 269-286.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Instability in diffusive ecological models with nonlocal delay effects
AU - Boushaba, Khalid
AU - Ruan, Shigui
PY - 2001/6/1
Y1 - 2001/6/1
N2 - We propose a reaction-diffusion system with nonlocal delays to model the growth of plankton communities feeding on a limiting nutrient supplied at a constant rate. Two delays are incorporated into the model: one describes the delayed nutrient recycling process and the other models the delayed growth response of the plankton. It is assumed that both delays are nonlocal in the sense that there are delayed not only in time but also in space. Local and bifurcation analyses are carried out. It has been shown that Turing-type spatial patterns occur when the diffusion coefficients vary and temporal or spatial-temporal patterns occur when the delay involved in the growth response changes.
AB - We propose a reaction-diffusion system with nonlocal delays to model the growth of plankton communities feeding on a limiting nutrient supplied at a constant rate. Two delays are incorporated into the model: one describes the delayed nutrient recycling process and the other models the delayed growth response of the plankton. It is assumed that both delays are nonlocal in the sense that there are delayed not only in time but also in space. Local and bifurcation analyses are carried out. It has been shown that Turing-type spatial patterns occur when the diffusion coefficients vary and temporal or spatial-temporal patterns occur when the delay involved in the growth response changes.
UR - http://www.scopus.com/inward/record.url?scp=0042232518&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0042232518&partnerID=8YFLogxK
U2 - 10.1006/jmaa.2000.7381
DO - 10.1006/jmaa.2000.7381
M3 - Article
AN - SCOPUS:0042232518
VL - 258
SP - 269
EP - 286
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
SN - 0022-247X
IS - 1
ER -