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A condition of the existence of stable positive steady-state solutions for a one predator two prey system

A condition of the existence of stable positive steady-state solutions for a one predator two... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics-A Journal of Chinese Universities Springer Journals

A condition of the existence of stable positive steady-state solutions for a one predator two prey system

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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

References

  • Bifurcation of steady-state solutions in predator-prey and competition systems
    J. Blat, K. J. Brown
  • Bifurcation, perturbation of simple eigenvalues, and linearized stability
    M. G. Grandall, P. H. Rabinrowitz
  • On positive solutions of some pairs of differential equations
    E. N. Dancer
  • Existence of steady-state solutions for a one predator two prey system
    N. Nacos
  • Equilibria and stabilities for competing species, reaction-diffusion equations with Dirichlet boundary data
    A. Leung
  • Bifurcation analysis of existence and stability of positive steady-state solutions for a one predator two prey system
    Song Kaitai, zhou Li
  • Stability of steady-state for prey-predator diffusion equations with homogeneous Dirichlet conditions
    Y. Yamada
  • Bifurcation method for coexistence analysis of competition diffusion system
    Zhou Li
  • Asymptotic behaviour of a competition diffusion system in population dynamics
    Zhou Li, C. V. Pao