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Global Behavior

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Abstract

This chapter is focused on the study of the global behavior of the nonlinear model discussed in the previous chapters. Actually, the stability results presented in Chap. 6 are restricted to the local perspective of looking on this side of the hedgerow while we set our aim on the ambitious goal of determining the behavior of solutions beyond the limits imposed by the linearization procedure. However, generally speaking, the problem of determining the global behavior of a system, i.e. of looking beyond the solitary hill of Leopardi, is not systematically settled but rather usually uses an approach that takes advantage of some special property exhibited by the system and rests upon methodologies that provide sufficient conditions for the analysis of that behavior.

Sempre caro mi fu quest’ermo colle,

E questa siepe, che da tanta parte

Dell’ultimo orizzonte il guardo esclude.

Ma sedendo e mirando, interminati

spazi di là da quella, e sovrumani

Silenzi, e profondissima quiete

Io nel pensier mi fingo; ove per poco

Il cor non si spaura …

G. Leopardi, L’infinito

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Notes

  1. 1.

    Since ever, I have loved so much this solitary hill,/ And this hedgerow that such a large part/ Of the farthest horizon, hides to the sight./ But sitting and watching, interminable/ paces beyond, and superhuman/ Silence, and profoundest stillness/ I pretend in my thoughts; where almost/ The heart is frightened …

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Authors and Affiliations

  1. Department of Mathematics, University of Trento, Trento, Italy

    Mimmo Iannelli

  2. School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona, USA

    Fabio Milner

Authors
  1. Mimmo Iannelli
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  2. Fabio Milner
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Iannelli, M., Milner, F. (2017). Global Behavior. In: The Basic Approach to Age-Structured Population Dynamics. Lecture Notes on Mathematical Modelling in the Life Sciences. Springer, Dordrecht. https://doi.org/10.1007/978-94-024-1146-1_8

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