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Global Dynamics of Discrete Dynamical Systems and Difference Equations

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Difference Equations, Discrete Dynamical Systems and Applications (ICDEA 2017)

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Abstract

We present a survey of new approaches to the investigation of the global dynamics of discrete dynamical systems or autonomous difference equations. To achieve our objectives, we have utilized singularity theory of Whitney, the notion of critical curves of Mira and Gardini, and the notion of the carrying simplex of Hirsch. Using a geometric approach, we extend the notion of monotonicity of Smith from planar systems to higher dimensional systems. The global dynamics of a special class of systems generated by triangular maps will be, thoroughly studied. Biological and economics models will be introduced to illustrate the effectiveness and applicability of our methods. Finally, we present some open problems and conjectures to stimulate more research in this area of paramount importance to the field of dynamical systems/difference equations.

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Authors and Affiliations

  1. Department of Mathematics, Trinity University, San Antonio, Texas, 78212-7200, USA

    Saber Elaydi

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  1. Saber Elaydi
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Correspondence to Saber Elaydi .

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Editors and Affiliations

  1. Department of Mathematics, Trinity University, San Antonio, TX, USA

    Saber Elaydi

  2. Institut für Mathematik, Alpen-Adria Universität Klagenfurt, Klagenfurt, Austria

    Christian Pötzsche

  3. Department of Mathematics, West University of TimiÅŸoara, TimiÅŸoara, Romania

    Adina Luminiţa Sasu

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Elaydi, S. (2019). Global Dynamics of Discrete Dynamical Systems and Difference Equations. In: Elaydi, S., Pötzsche, C., Sasu, A. (eds) Difference Equations, Discrete Dynamical Systems and Applications. ICDEA 2017. Springer Proceedings in Mathematics & Statistics, vol 287. Springer, Cham. https://doi.org/10.1007/978-3-030-20016-9_3

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