Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/a-condition-of-the-existence-of-stable-positive-steady-state-solutions-7SvklCBWeb
References (11)
-
Nela Lakoš (1990)
Existence of steady-state solutions for a one-predator-two prey systemSiam Journal on Mathematical Analysis, 21
-
A. Leung (1980)
Equilibria and stabilities for competing-species reaction-diffusion equations with Dirichlet boundary dataJournal of Mathematical Analysis and Applications, 73
-
Zhou Li (1991)
Bifurcation method for coexistence analysis of competition diffusion systemActa Math. Appl. Sinica, 14
-
M. Crandall, P. Rabinowitz (1973)
Bifurcation, perturbation of simple eigenvalues, itand linearized stabilityArchive for Rational Mechanics and Analysis, 52
-
E. N. Dancer (1984)
On positive solutions of some pairs of differential equationsTrans. Amer. Math. Soc., 284
-
H-M Xie (1993)
ON DENSITY OF SMOOTH ELEMENTS FOR AN ACTION OF AN AMENABLE GROUPActa Mathematica Scientia, 13
-
Yoshio Yamada (1990)
Stability of steady states for prey-predator diffusion equations with homogeneous dirichlet conditionsSiam Journal on Mathematical Analysis, 21
-
Kaitai Song, Li Zhou (1993)
THE BIFURCATION ANALYSIS OF EXISTENCE AND STABILITY OF POSITIVE STEADY-STATE SOLUTION FOR A ONE-PREDATOR-TWO-PREY SYSTEMActa Mathematica Scientia, 13
-
E. Dancer (1984)
On positive solutions of some pairs of differential equationsTransactions of the American Mathematical Society, 284
-
L. Zhou, C. Pao (1982)
Asymptotic behavior of a competition—diffusion system in population dynamicsNonlinear Analysis-theory Methods & Applications, 6
-
J. Blat, K. Brown (1984)
Bifurcation of steady-state solutions in predator-prey and competition systemsProceedings of the Royal Society of Edinburgh: Section A Mathematics, 97
- Publisher
- Springer Journals
- Copyright
- 1993 Editorial Committee of Applied Mathematics-A Journal of Chinese Universities
- ISSN
- 1005-1031
- eISSN
- 1993-0445
- DOI
- 10.1007/BF02661996
- Publisher site
- See Article on Publisher Site
Abstract
Abstract One predator two prey system is a research topic which has both the theoretical and practical values. This paper provides a natural condition of the existence of stable positive steady-state solutions for the one predator two prey system. Under this condition we study the existence of the positive steady-state solutions at vicinity of the triple eigenvalue by implicit function theorem, discuss the positive stable solution problem bifurcated from the semi-trivial solutions containing two positive components with the help of bifurcation and perturbation methods.
Journal
Applied Mathematics-A Journal of Chinese Universities – Springer Journals
Published: Dec 1, 1993