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Periodic solutions of third order predator-prey equations simulating an immune response

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References

  1. Bell, George, I., “Mathematical model of clonal selection and antibody production,” in three parts, Journal of Theoretical Biology, Vol. 29, pp. 191–232 (1970), Vol. 33, pp. 339–378, Vol. 33, pp. 379–398 (1971).

    Google Scholar 

  2. Bell, George, I., Mathematical model of clonal selection and antibody production. Nature 228, No. 5273, pp. 739–744 (1970).

    Google Scholar 

  3. Bell, George, I., Predator-prey equations simulating an immune response. Mathematical Biosciences, an International Journal 16, pp. 291–314 (1973).

    Google Scholar 

  4. Friedrichs, K. O., Lectures on Advanced Ordinary Differential Equations. New York University Lecture Notes, 1948–49, 1954.

  5. Hopf, E., Abzweigung einer periodischen Lösung eines Differentialsystems. Berichte der Mathematisch-Physicalischen Klasse der Sächsischen Akademie der Wissenschaften zu Leipzig XCIV, 3–22 (1942).

  6. Joseph, D. D., & D. H. Sattinger, Bifurcating time periodic solutions and their stability. Archive for Rational Mechanics and Analysis 45, No. 2, pp. 79–109 (1972).

    Google Scholar 

  7. Lefschetz, S., Differential Equations; Geometric Theory. New York: Interscience Publishers, Inc. 1957.

    Google Scholar 

  8. Pimbley, G. H., Jr., Periodic solutions of predator-prey equations simulating an immune response I. To appear in Mathematical Biosciences, an International Journal, 1974.

  9. Pimbley, G. H., Jr., Periodic solutions of predator-prey equations simulating an immune response II. To appear in Mathematical Biosciences, an International Journal, 1974.

  10. Pimbley, G. H., On Predator-Prey Equations Simulating an Immune Response. Proceedings of Meeting on Application of Mathematical Methods to Nonlinear Problems, Seattle, 1972; Springer Lecture Notes in Mathematics, Vol. 322, pp. 231–243.

  11. Poincaré, H., Collected Works, Vol. I. Paris: Gauthier-Villars et Cie 1951.

    Google Scholar 

  12. Sattinger, D. H., Topics in Stability and Bifurcation Theory. Lecture Notes in Mathematics, Vol. 309. Berlin, Heidelberg, New York: Springer 1973.

    Google Scholar 

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Communicated by R. Aris

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Pimbley, G.H. Periodic solutions of third order predator-prey equations simulating an immune response. Arch. Rational Mech. Anal. 55, 93–123 (1974). https://doi.org/10.1007/BF00249934

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