Abstract
This paper studies the stationary solutions of a prey–predator model with population flux by attractive transition. We first obtain a bifurcation branch (connected set) of positive solutions which connects two semitrivial solutions. Next we derive the asymptotic behavior of positive solutions as the coefficient α of the population flux tends to infinity. A main result implies that positive solutions can be classified into two types as α→∞. In one type of them, as α→∞, positive solutions of the prey–predator model approach positive solutions of a competition model with equal diffusion coefficients.
| Original language | English |
|---|---|
| Pages (from-to) | 589-615 |
| Number of pages | 27 |
| Journal | Nonlinear Analysis: Real World Applications |
| Volume | 44 |
| DOIs | |
| Publication status | Published - 2018 Dec 1 |
| Externally published | Yes |
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Keywords
- A priori estimate
- Asymptotic behavior
- Attractive transitional flux
- Bifurcation analysis
- Coexistence steady states
- Prey–predator model
ASJC Scopus subject areas
- Analysis
- Engineering(all)
- Economics, Econometrics and Finance(all)
- Computational Mathematics
- Applied Mathematics
Cite this
Positive steady states for a prey–predator model with population flux by attractive transition. / Oeda, Kazuhiro; Kuto, Kousuke.
In: Nonlinear Analysis: Real World Applications, Vol. 44, 01.12.2018, p. 589-615.Research output: Contribution to journal › Article
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TY - JOUR
T1 - Positive steady states for a prey–predator model with population flux by attractive transition
AU - Oeda, Kazuhiro
AU - Kuto, Kousuke
PY - 2018/12/1
Y1 - 2018/12/1
N2 - This paper studies the stationary solutions of a prey–predator model with population flux by attractive transition. We first obtain a bifurcation branch (connected set) of positive solutions which connects two semitrivial solutions. Next we derive the asymptotic behavior of positive solutions as the coefficient α of the population flux tends to infinity. A main result implies that positive solutions can be classified into two types as α→∞. In one type of them, as α→∞, positive solutions of the prey–predator model approach positive solutions of a competition model with equal diffusion coefficients.
AB - This paper studies the stationary solutions of a prey–predator model with population flux by attractive transition. We first obtain a bifurcation branch (connected set) of positive solutions which connects two semitrivial solutions. Next we derive the asymptotic behavior of positive solutions as the coefficient α of the population flux tends to infinity. A main result implies that positive solutions can be classified into two types as α→∞. In one type of them, as α→∞, positive solutions of the prey–predator model approach positive solutions of a competition model with equal diffusion coefficients.
KW - A priori estimate
KW - Asymptotic behavior
KW - Attractive transitional flux
KW - Bifurcation analysis
KW - Coexistence steady states
KW - Prey–predator model
UR - http://www.scopus.com/inward/record.url?scp=85049075291&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85049075291&partnerID=8YFLogxK
U2 - 10.1016/j.nonrwa.2018.06.006
DO - 10.1016/j.nonrwa.2018.06.006
M3 - Article
AN - SCOPUS:85049075291
VL - 44
SP - 589
EP - 615
JO - Nonlinear Analysis: Real World Applications
JF - Nonlinear Analysis: Real World Applications
SN - 1468-1218
ER -