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Bifurcation in a quartic polynomial system arising in biology

Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1455)

Keywords

Vector Field Hopf Bifurcation Phase Portrait Double Root Transcritical Bifurcation 
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. 1.
    A. A. Andronov, E. A. Leontovich, I. I. Gordon, and A. G. Maier, “Theory of Bifurcations of Dynamic Systems on a Plane,” Israel Program for Scientific Translations, John Wiley & Sons, New York, 1973.Google Scholar
  2. 2.
    A. A. Andronov, E. A. Leontovich, I. I. Gordon, and A. G. Maier, “Qualitative Theory of Second-Order Dynamic Systems,” Israel Program for Scientific Translations, John Wiley & Sons, New York, 1973.Google Scholar
  3. 3.
    C. Chicone and D. S. Shafer, Separatrix and limit cycles of quadratic systems and a theorem of Dulac, Trans. Amer. Math. Soc. 278 (1983), 585–612.MathSciNetzbMATHGoogle Scholar
  4. 4.
    H. I. Freedman, “Deterministic Mathematical Models in Population Ecology,” Marcel Dekker, New York, 1980.zbMATHGoogle Scholar
  5. 5.
    J. Guckenheimer and P. Holmes, “Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields,” Springer-Verlag, New York, 1983.CrossRefzbMATHGoogle Scholar
  6. 6.
    N. Kopell and I. N. Howard, Bifurcations and trajectories joining critical points, Adv. in Math. 18 (1975), 306–358.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    J. E. Marsden and M. McCracken, “The Hopf Bifurcation and Its Applications,” Springer-Verlag, New York, 1976.CrossRefzbMATHGoogle Scholar
  8. 8.
    H. I. Freedman and G. S. K. Wolkowocz, Predator-Prey systems with group defence: the paradox of enrichment revisited, Bull. Math. Biol. 48 (1986), 493–508. [not cited].MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  1. 1.Mathematics DepartmentUniversity of North Carolina at CharlotteCharlotteUSA

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