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

Ladas, G.; Kocic, V.L.

 
9780792322863: Global Behavior of Nonlinear Difference Equations of Higher Order with Applications: 256 (Mathematics and Its Applications, 256)
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ISBN 10: 079232286X ISBN 13: 9780792322863
Editorial: Springer, 1993

Sinopsis

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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Reseña del editor

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.

Reseña del editor

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 very frontiers of the subject, important 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 includes notes and references. The volume concludes with three appendices, a comprehensive bibliography, and name and subject indices.
For graduate students and researchers whose work involves difference and differential equations.

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Editorial
Springer
Año de publicación
1993
Idioma
Inglés
ISBN 10 
079232286X
ISBN 13 
9780792322863
Encuadernación
Tapa dura
Número de páginas
244
Contacto del fabricante
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Heidelberg
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Alemania

Otras ediciones populares con el mismo título

9789048142736: Global Behavior of Nonlinear Difference Equations of Higher Order with Applications: 256 (Mathematics and Its Applications)

Edición Destacada

ISBN 10:  9048142733 ISBN 13:  9789048142736
Editorial: Springer, 2010
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