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On predator-prey equations simulating an immune response

Part of the Lecture Notes in Mathematics book series (LNM,volume 322)

Keywords

  • Periodic Solution
  • Constant Solution
  • Time Periodic Solution
  • Bifurcation Theorem
  • Positive Quadrant

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References

  1. Bell, George I., "Mathematical Model of Clonal Selection and Antibody Production," Journal of Theoretical Biology, 33, 339 (1971).

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  2. Bell, George I., "Predator-Prey Equations Simulating an Immune Response," to be published in Mathematical Biosciences: An International Journal.

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  3. Coddington, E. A. and Levinson, N., Theory of Ordinary Differential Equations (McGraw-Hill Publ. Co., New York, 1955).

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  4. Friedrichs, K. O., Lectures on Advanced Ordinary Differential Equations, New York University Lecture Notes, 1948–1949.

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  5. Hopf, E., "Abzweigung einer periodischen Lösung eines Differentialsystems," Aus den Berichten der Mathematisch-Physikalischen Klasse der Sächsischen Akademie der Wissen-schaften zu Leipzig XCIV, 1–22 (1942).

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  6. Joseph, D. D. and Sattinger, D. H., "Bifurcating Time Periodic Solutions and Their Stability," Arch. for Rational Mech. and Anal., 45, No. 2, 79–109 (1972).

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  7. Sattinger, D. H., "Stability of Bifurcating Solutions by Leray-Schauder Degree," Arch. for Rational Mech. and Anal., 43, 154–166 (1971).

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  8. Sattinger D. H., Topics in Stability and Bifurcation Theory, Springer Lecture Note Series, No. 309, 1973.

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  9. Waltman, P. E., "The Equations of Growth," Bulletin of Mathematical Biophysics, 26, 39–43 (1964).

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© 1973 Springer Verlag

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Pimbley, G.H. (1973). On predator-prey equations simulating an immune response. In: Stakgold, I., Joseph, D.D., Sattinger, D.H. (eds) Nonlinear Problems in the Physical Sciences and Biology. Lecture Notes in Mathematics, vol 322. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0060569

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  • DOI: https://doi.org/10.1007/BFb0060569

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06251-6

  • Online ISBN: 978-3-540-38558-5

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