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
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)
Brauer, F., Nohel, J.A.: The Qualitative Theory of Ordinary Differential Equations: An Introduction. Dover Publications, New York (1989)
Coddington, E.A., Levinson, N.: Theory of Ordinary Differential Equations. McGraw-Hill, New York (1955)
Hirsch, M.W., Smale, S.: Differential Equations, Dynamical Systems and Linear Algebra. Academic Press, New York (1974)
Hirsch, M.W., Smale, S., Devaney, R.L.: Differential Equations, Dynamical Systems & an Introduction to Chaos. 2nd ed., Elsevier, New York (2004)
Kuznetsov, Y.A.: Elements of Applied Bifurcation Theory, Springer, New York (2010)
Perko, L.: Differential Equations and Dynamical Systems. 3rd ed., Springer, New York (1996)
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)
Smith, H.L., Thieme, H.R.: Dynamical Systems and Population Persistence. Graduate Studies in Mathematicas 118, American Mathematical Soc. (2011)
Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos. Springer, New York (1990)
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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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DOI: https://doi.org/10.1007/978-3-319-03026-5_10
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