Global Behavior of Nonlinear Difference Equations of Higher Order with Applications: 256 (Mathematics and Its Applications, 256) - Hardcover

Kocic, V.L.; Ladas, G.

Hardcover

ISBN 10: 079232286X ISBN 13: 9780792322863

Publisher: Springer, 1993

Synopsis

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.

About this title

Synopsis

This volume presents a systematic study of the global behaviour of solutions of nonlinear scalar difference equations of order greater than one. Of particular interest are aspects such as global asymptotic stability, periodicity, permanence and persistence, and also semicycles of solutions. As well as exposing the reader to the frontiers of the subject, open problems are also formulated. The book has six chapters. Chapter 1 presents an introduction to the subject and deals with preliminaries. Chapter 2 considers global stability results. Chapter 3 is devoted to rational recursive structures. Chapter 4 describes various applications. The topic of Chapter 5 is periodic cycles, and Chapter 6 discusses a number of open problems and conjectures involving interesting types of difference equations. Each chapter in cludes notes and references. The volume concludes with three appendices, a comprehensive bibliography, and name and subject indexes. This text is designed for graduate students and researchers whose work involves difference and differential equations.

Edition details

• Publisher: Springer
• Publication date: 1993
• Language: English
• ISBN 10: 079232286X
• ISBN 13: 9780792322863
• Binding: Hardcover
• Number of pages: 240