Existence, uniqueness and stability of positive steady states to a prey-predator diffusion system

被引：0

作者：

WANG MingXin1

机构：

来源：

Science China Mathematics | 2009年 / 05期

基金：

中国国家自然科学基金;

关键词：

preypredator model; positive solutions; bifurcation; existence and uniqueness; stability;

D O I：

暂无

中图分类号：

O175 [微分方程、积分方程];

学科分类号：

070104 ;

摘要：

In the paper, we study the positive solutions of an elliptic system coming from a preypredator model with modified Leslie-Gower and Holling-Type II schemes. We study the existence, non-existence, bifurcation, uniqueness and stability of positive solutions. In particular, we obtain a continuum of positive solutions connecting a semitrivial solution to the unique positive solution of the limiting system.

引用

页码：1031 / 1041

页数：11

共 11 条

[1] Minimal complexity of semi-bounded components in bifurcation theory[J] . Julián López-Gómez,Carlos Mora-Corral.Nonlinear Analysis . 2004 (7)
[2] Boundedness and global stability for a predator-prey model with modified Leslie-Gower and Holling-type II schemes
Aziz-Alaoui, MA
Okiye, MD
[J]. APPLIED MATHEMATICS LETTERS, 2003, 16 (07) : 1069 - 1075
[3] On the Symbiotic Lotka–Volterra Model with Diffusion and Transport Effects[J] . M. Delgado,J. López-Gómez,A. Suárez.Journal of Differential Equations . 2000 (1)
[4] S-Shaped Global Bifurcation Curve and Hopf Bifurcation of Positive Solutions to a Predator–Prey Model[J] . Yihong Du,Yuan Lou.Journal of Differential Equations . 1998 (2)
[5] Some uniqueness and exact multiplicity results for a predator-prey model
Du, YH
Lou, Y
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1997, 349 (06) : 2443 - 2475
[6] POSITIVE STEADY-STATE SOLUTIONS OF A COMPETING REACTION-DIFFUSION SYSTEM
RUAN, WH
PAO, CV
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1995, 117 (02) : 411 - 427
[7] On the fixed point index and multiple steady-state solutions of reaction-diffusion systems[J] . Weihua Ruan,Wei Feng.Differential and Integral Equations . 1995 (2)
[8] COEXISTENCE THEOREMS OF STEADY-STATES FOR PREDATOR-PREY INTERACTING SYSTEMS
LI, LG
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1988, 305 (01) : 143 - 166
[9] FIXED-POINT EQUATIONS AND NONLINEAR EIGENVALUE PROBLEMS IN ORDERED BANACH-SPACES
AMANN, H
[J]. SIAM REVIEW, 1976, 18 (04) : 620 - 709
[10] Bifurcation, perturbation of simple eigenvalues, itand linearized stability[J] . Michael G. Crandall,Paul H. Rabinowitz.Archive for Rational Mechanics and Analysis . 1973 (2)

← 1 2 →