Title: Global Behavior of Nonlinear Difference Equations of Higher Order with Applications (Mathematics and Its Applications, 256)
Publisher: Springer
Publication Date: 1993
Language: English
ISBN 10: 079232286X
ISBN 13: 9780792322863
Binding: Hardcover
Condition: New

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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.

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