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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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Contenuti
Preface. 1. Introduction and Preliminaries. 2. Global Stability Results. 3. Rational Recursive Sequences. 4. Applications. 5. Periodic Cycles. 6. Open Problems and Conjectures. Appendix: A. The Riccati Difference Equation. B. A Generalized Contraction Principle. C. Global Behaviour of Systems of Nonlinear Difference Equations. Bibliography. Subject Index. Author Index.
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Global Behavior of Nonlinear Difference Equations of Higher Order with Applications (Mathematics and Its Applications)
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Global Behavior of Nonlinear Difference Equations of Higher Order with Applications
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Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 244 pp. Englisch. Codice articolo 9789048142736
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Global Behavior of Nonlinear Difference Equations of Higher Order with Applications
Editore:
Springer, Springer Dez 2010, 2010
ISBN 10: 9048142733
ISBN 13: 9789048142736
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Taschenbuch. Condizione: Neu. This item is printed on demand - Print on Demand Titel. Neuware -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.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 244 pp. Englisch. Codice articolo 9789048142736
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