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Global Behavior of Nonlinear Difference Equations of Higher Order with Applications

  • V. L. Kocic
  • G. Ladas

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

Table of contents

  1. Front Matter
    Pages i-xi
  2. V. L. Kocic, G. Ladas
    Pages 1-26
  3. V. L. Kocic, G. Ladas
    Pages 27-54
  4. V. L. Kocic, G. Ladas
    Pages 55-74
  5. V. L. Kocic, G. Ladas
    Pages 75-132
  6. V. L. Kocic, G. Ladas
    Pages 133-152
  7. V. L. Kocic, G. Ladas
    Pages 153-176
  8. Back Matter
    Pages 177-228

About this book

Introduction

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.

Keywords

behavior difference equation differential equation stability

Authors and affiliations

  • V. L. Kocic
    • 1
  • G. Ladas
    • 1
  1. 1.Department of MathematicsUniversity of Rhode IslandKingstonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-017-1703-8
  • Copyright Information Springer Science+Business Media B.V. 1993
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-4273-6
  • Online ISBN 978-94-017-1703-8
  • Buy this book on publisher's site