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Bifurcation in a quartic polynomial system arising in biology

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Bifurcations of Planar Vector Fields

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

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References

  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.

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  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. 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.

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  4. H. I. Freedman, “Deterministic Mathematical Models in Population Ecology,” Marcel Dekker, New York, 1980.

    MATH  Google Scholar 

  5. J. Guckenheimer and P. Holmes, “Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields,” Springer-Verlag, New York, 1983.

    Book  MATH  Google Scholar 

  6. N. Kopell and I. N. Howard, Bifurcations and trajectories joining critical points, Adv. in Math. 18 (1975), 306–358.

    Article  MathSciNet  MATH  Google Scholar 

  7. J. E. Marsden and M. McCracken, “The Hopf Bifurcation and Its Applications,” Springer-Verlag, New York, 1976.

    Book  MATH  Google Scholar 

  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].

    Article  MathSciNet  MATH  Google Scholar 

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Jean-Pierre Françoise Robert Roussarie

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© 1990 Springer-Verlag

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Rothe, F., Shafer, D.S. (1990). Bifurcation in a quartic polynomial system arising in biology. In: Françoise, JP., Roussarie, R. (eds) Bifurcations of Planar Vector Fields. Lecture Notes in Mathematics, vol 1455. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0085400

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  • DOI: https://doi.org/10.1007/BFb0085400

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  • Print ISBN: 978-3-540-53509-6

  • Online ISBN: 978-3-540-46722-9

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