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Global Behavior of Nonlinear Difference Equations of Higher Order with Applications : Fluid Mechanics and Its Applications - V.L. Kocic

Global Behavior of Nonlinear Difference Equations of Higher Order with Applications

Fluid Mechanics and Its Applications

Hardcover Published: 31st May 1993
ISBN: 9780792322863
Number Of Pages: 228

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Nonlinear difference equations of order greater than one are of paramount imporĀ­ 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.

Introduction and Preliminariesp. 1
Global Stability Resultsp. 27
Rational Recursive Sequencesp. 55
Applicationsp. 75
Periodic Cyclesp. 133
Open Problems and Conjecturesp. 153
App. A The Riccati Difference Equationp. 177
App. B A Generalized Contraction Principlep. 189
App. C Global Behavior of Systems of Nonlinear Difference Equationsp. 195
Bibliographyp. 205
Subject Indexp. 223
Author Indexp. 225
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792322863
ISBN-10: 079232286X
Series: Fluid Mechanics and Its Applications
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 228
Published: 31st May 1993
Country of Publication: NL
Dimensions (cm): 23.39 x 15.6  x 1.42
Weight (kg): 0.52