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Global Behavior of Nonlinear Difference Equations of Higher Order with Applications

  • Book
  • © 1993

Overview

Authors:
  1. V. L. Kocic

    1. Department of Mathematics, University of Rhode Island, Kingston, USA

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    You can also search for this author in PubMed   Google Scholar

  2. G. Ladas

    1. Department of Mathematics, University of Rhode Island, Kingston, USA

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Mathematics and Its Applications (MAIA, volume 256)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xi
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  2. Introduction and Preliminaries

    • V. L. Kocic, G. Ladas
    Pages 1-26

  3. Global Stability Results

    • V. L. Kocic, G. Ladas
    Pages 27-54

  4. Rational Recursive Sequences

    • V. L. Kocic, G. Ladas
    Pages 55-74

  5. Applications

    • V. L. Kocic, G. Ladas
    Pages 75-132

  6. Periodic Cycles

    • V. L. Kocic, G. Ladas
    Pages 133-152

  7. Open Problems and Conjectures

    • V. L. Kocic, G. Ladas
    Pages 153-176

  8. Back Matter

    Pages 177-228
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Keywords

About this book

Nonlinear difference equations of order greater than one are of paramount impor­ tance in applications where the (n + 1)st generation (or state) of the system depends on the previous k generations (or states). Such equations also appear naturally as discrete analogues and as numerical solutions of differential and delay differential equations which model various diverse phenomena in biology, ecology, physiology, physics, engineering and economics. Our aim in this monograph is to initiate a systematic study of the global behavior of solutions of nonlinear scalar difference equations of order greater than one. Our primary concern is to study the global asymptotic stability of the equilibrium solution. We are also interested in whether the solutions are bounded away from zero and infinity, in the description of the semi cycles of the solutions, and in the existence of periodic solutions. This monograph contains some recent important developments in this area together with some applications to mathematical biology. Our intention is to expose the reader to the frontiers of the subject and to formulate some important open problems that require our immediate attention.

Authors and Affiliations

  • Department of Mathematics, University of Rhode Island, Kingston, USA

    V. L. Kocic, G. Ladas

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