Segregation Structures of Competing Species Mediated by a Diffusive Predator

  • Y. Kan-on
  • M. Mimura
Part of the Lecture Notes in Biomathematics book series (LNBM, volume 71)

Abstract

It has been suggested that, in some circumstances, predation may tend to increase species diversity in competitive communities, which is the so called predator-mediated coexistence hypothesis.

Keywords

Equilibrium Point Hopf Bifurcation Prey Species Solution Branch Bifurcation Curve 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. J. H. Connell, A predator-prey system in the marine intertidal region. I. Balanus gianduia and several predator species of thais, Ecol. Monogr. 40, 1970, 49–78.CrossRefGoogle Scholar
  2. E. Conway, D. Hoff and J. Smoller, Large time behavior of solutions of systems of nonlinear reaction-diffusion equations, SIAM J. Appl. Math. 35, 1978, 1–16.CrossRefMATHMathSciNetGoogle Scholar
  3. H. Fujii, M. Mimura and Y. Nishiura, A picture of global diagram in ecological interacting and diffusing systems, Physica 5D, 1982, 1–42.MathSciNetGoogle Scholar
  4. K. Fujii, Complexity-stability relatioship of two-prey-one-predator species system model: Local and global stability, J. Theoret. Bio. 69, 1977, 613–623.CrossRefGoogle Scholar
  5. J. L. Harper, The role of predation in vegetational diversity, in Diversity and Stability in Ecological Systems (G.M. Woodwell and H. H. Smith, Eds), Brookhaven National Laboratory, Upton, N. Y., 1969, 48–62.Google Scholar
  6. S. B. Hsu, On general two-species competition model with diffusion, preprint.Google Scholar
  7. S. B. Hsu, Predator-mediated coexistence and extinction, Math. Biosci. 54, 1980, 231–269.CrossRefGoogle Scholar
  8. V. Hutson and G. T. Vickers, A criterion for permanent coexistence of species with an application to a two-prey one-predator system, Math. Biosci. 63, 1983, 252–269.CrossRefMathSciNetGoogle Scholar
  9. K. Kawasaki and E. Teramoto, Private communication.Google Scholar
  10. R. M. May, Stability in multispecies community models, Math. Biosci. 12, 1971, 59–79.CrossRefMATHMathSciNetGoogle Scholar
  11. M. Mimura and P. C. Fife, A 3-component system of competition and diffusion, Hiroshima Math. J. 16, 1986, 189–207.MATHMathSciNetGoogle Scholar
  12. M. Mimura and Y. Kan-on, Predation-mediated coexistence and segregation structures, in Patterns and Waves (T. Nishida, M. Mimura and H. Fujii, Eds), Kinokuniya/North-Holland, 1986, 129–155.Google Scholar
  13. P. de Mottoni, Qualitative analysis for some quasi-linear parabolic systems, Institute of Math. Polish Academy of Sci. Zam 11/79, 1979.Google Scholar
  14. R. T. Paine, Food web complexity and species diversity, Amer. Natur. 100, 1966, 65–75.CrossRefGoogle Scholar
  15. J. D. Parrish and S. B. Saila, Interspecific competition, predation an and species diversity, J. Theoret. Biol. 27, 1970, 207–220.CrossRefGoogle Scholar
  16. Y. Takeuchi and N. Adachi, Existence and bifurcation of stable equilibrium in two-prey, one-predator communities, Bull. Math. Biol. 45, 1983, 877–900.MATHMathSciNetGoogle Scholar
  17. R. R. Vance, Predator and resource partitioning in one predator-two prey model communities, Amer. Natur. 112, 1978, 797–813.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Y. Kan-on
    • 1
  • M. Mimura
    • 2
  1. 1.Hiroshima National College of Maritime TechnologyJapan
  2. 2.Department of MathematicsHiroshima UniversityJapan

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