Acta Applicandae Mathematica

, Volume 14, Issue 1–2, pp 49–57 | Cite as

Cooperative systems theory and global stability of diffusion models

  • Y. Takeuchi
I. Stability and Persistence for Ecological Models

AMS Subject Classification (1980)

92A17 34D20 

Key words

global stability cooperative systems diffusion 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Allen L.J.S. (1987), Persistence, extinction, and critical patch number for island populations, J. Math. Biol., 24, 617–625.Google Scholar
  2. [2]
    Beretta E. and Takeuchi Y. (1987), Global stability of single-species diffusion models with continuous time delays, Bull. Math. Biol., 49, No. 4, 431–448.Google Scholar
  3. [3]
    Beretta E. and Takeuchi Y. (1988), Global asymptotic stability of Lotka-Volterra diffusion models with continuous time delay, SIAM J. Appl. Math., 48, No. 3, 627–651Google Scholar
  4. [4]
    Freedman H.I., Rai B., and Waltman P. (1986), Mathematical models of population interactions with dispersal II: Differential survival in a change of habitat, J. Math. Anal. Appl., 115, 140–154.Google Scholar
  5. [5]
    Hadeler K.P. and Glas D. (1983), Quasimonotone systems and convergence to equilibrium in a population genetic model, J. Math. Anal. Appl., 95, 297–303.Google Scholar
  6. [6]
    Hastings A. (1982), Dynamics of a single species in a spatially varying environment: The stabilizing role of higher dispersal rates, J. Math. Biol., 16, 49–55.Google Scholar
  7. [7]
    Hirsch M.W. (1984), The dynamical systems approach to differential equations, Bull. A.M.S., 11, No. 1, 1–634.Google Scholar
  8. [8]
    Kamke E. (1932), Zur Theorie der Systeme gewöhnlicher Differentialgleichungen II, Acta Math., 58, 57–85.Google Scholar
  9. [9]
    Nikaido H. (1968), Convex structure and economic theory, Academic Press, New York - London.Google Scholar
  10. [10]
    Smith H.L. (1986), On the asymptotic behavior of a class of deterministic models of cooperating species, SIAM J. Appl. Math., 46, 368–375.Google Scholar

Copyright information

© IIASA 1989

Authors and Affiliations

  • Y. Takeuchi
    • 1
  1. 1.Department of Applied Mathematics Faculty of EngineeringShizuoka UniversityHamamatsuJapan

Personalised recommendations