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Basic theory of Ordinary Differential Equations

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An Introduction to Mathematical Population Dynamics

Part of the book series: UNITEXT ((UNITEXTMAT,volume 79))

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Abstract

Differential Equations are somewhat pervasive in the description of natural phenomena and the theory of Ordinary Differential Equations is a basic framework where concepts, tools and results allow a systematic approach to knowledge. This same book aims to give a concrete proof of how the modeling of Nature is based on this theory and beyond. This appendix is intended to provide some concepts and results that are used in the text, referring to the student background and to textbooks for a full acquaintance of the material. We actually mention [2,3,5,7,10] as basic references on the subject.

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References

  1. Boldin, B.: Introducing a population into a steady community: The critical case, the center manifold, and the direction of bifurcation. SIAM J. Appl. Math. 66, 1424–1453 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  2. Brauer, F., Nohel, J.A.: The Qualitative Theory of Ordinary Differential Equations: An Introduction. Dover Publications, New York (1989)

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

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  4. Hirsch, M.W., Smale, S.: Differential Equations, Dynamical Systems and Linear Algebra. Academic Press, New York (1974)

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  5. Hirsch, M.W., Smale, S., Devaney, R.L.: Differential Equations, Dynamical Systems & an Introduction to Chaos. 2nd ed., Elsevier, New York (2004)

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  6. Kuznetsov, Y.A.: Elements of Applied Bifurcation Theory, Springer, New York (2010)

    Google Scholar 

  7. Perko, L.: Differential Equations and Dynamical Systems. 3rd ed., Springer, New York (1996)

    Book  MATH  Google Scholar 

  8. Smith, H.L.: Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems. Mathematical Surveys and Monographs 41, American Mathematical Soc. (2008)

    Google Scholar 

  9. Smith, H.L., Thieme, H.R.: Dynamical Systems and Population Persistence. Graduate Studies in Mathematicas 118, American Mathematical Soc. (2011)

    Google Scholar 

  10. Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos. Springer, New York (1990)

    Book  MATH  Google Scholar 

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Iannelli, M., Pugliese, A. (2014). Basic theory of Ordinary Differential Equations. In: An Introduction to Mathematical Population Dynamics. UNITEXT(), vol 79. Springer, Cham. https://doi.org/10.1007/978-3-319-03026-5_10

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