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Global Behavior of Nonlinear Difference Equations of Higher Order with Applications

2013-03-09 Mathematics
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Release : 2013-03-09
Genre : Mathematics
Kind : eBook
Book Rating : 036/5 ( reviews)

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Book Synopsis Global Behavior of Nonlinear Difference Equations of Higher Order with Applications by : V.L. Kocic

Download or read book Global Behavior of Nonlinear Difference Equations of Higher Order with Applications written by V.L. Kocic. This book was released on 2013-03-09. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Global Behavior of Nonlinear Difference Equations

2004 Nonlinear difference equations
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Release : 2004
Genre : Nonlinear difference equations
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Book Synopsis Global Behavior of Nonlinear Difference Equations by : Cathy Ann Clark

Download or read book Global Behavior of Nonlinear Difference Equations written by Cathy Ann Clark. This book was released on 2004. Available in PDF, EPUB and Kindle. Book excerpt:

Global Behavior of Some Nonlinear Difference Equations

2003 Nonlinear difference equations
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Release : 2003
Genre : Nonlinear difference equations
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Book Synopsis Global Behavior of Some Nonlinear Difference Equations by : Mihaela O. Predescu

Download or read book Global Behavior of Some Nonlinear Difference Equations written by Mihaela O. Predescu. This book was released on 2003. Available in PDF, EPUB and Kindle. Book excerpt:

Nonlinear Difference Equations

2013-03-14 Mathematics
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Release : 2013-03-14
Genre : Mathematics
Kind : eBook
Book Rating : 171/5 ( reviews)

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Book Synopsis Nonlinear Difference Equations by : H. Sedaghat

Download or read book Nonlinear Difference Equations written by H. Sedaghat. This book was released on 2013-03-14. Available in PDF, EPUB and Kindle. Book excerpt: It is generally acknowledged that deterministic formulations of dy namical phenomena in the social sciences need to be treated differently from similar formulations in the natural sciences. Social science phe nomena typically defy precise measurements or data collection that are comparable in accuracy and detail to those in the natural sciences. Con sequently, a deterministic model is rarely expected to yield a precise description of the actual phenomenon being modelled. Nevertheless, as may be inferred from a study of the models discussed in this book, the qualitative analysis of deterministic models has an important role to play in understanding the fundamental mechanisms behind social sci ence phenomena. The reach of such analysis extends far beyond tech nical clarifications of classical theories that were generally expressed in imprecise literary prose. The inherent lack of precise knowledge in the social sciences is a fun damental trait that must be distinguished from "uncertainty. " For in stance, in mathematically modelling the stock market, uncertainty is a prime and indispensable component of a model. Indeed, in the stock market, the rules are specifically designed to make prediction impossible or at least very difficult. On the other hand, understanding concepts such as the "business cycle" involves economic and social mechanisms that are very different from the rules of the stock market. Here, far from seeking unpredictability, the intention of the modeller is a scientific one, i. e.

Periodicities in Nonlinear Difference Equations

2004-12-16 Mathematics
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Release : 2004-12-16
Genre : Mathematics
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Book Rating : 560/5 ( reviews)

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Book Synopsis Periodicities in Nonlinear Difference Equations by : E.A. Grove

Download or read book Periodicities in Nonlinear Difference Equations written by E.A. Grove. This book was released on 2004-12-16. Available in PDF, EPUB and Kindle. Book excerpt: Sharkovsky's Theorem, Li and Yorke's "period three implies chaos" result, and the (3x+1) conjecture are beautiful and deep results that demonstrate the rich periodic character of first-order, nonlinear difference equations. To date, however, we still know surprisingly little about higher-order nonlinear difference equations. During the last ten years, the authors of this book have been fascinated with discovering periodicities in equations of higher order which for certain values of their parameters have one of the following characteristics: 1. Every solution of the equation is periodic with the same period. 2. Every solution of the equation is eventually periodic with a prescribed period. 3. Every solution of the equation converges to a periodic solution with the same period. This monograph presents their findings along with some thought-provoking questions and many open problems and conjectures worthy of investigation. The authors also propose investigation of the global character of solutions of these equations for other values of their parameters and working toward a more complete picture of the global behavior of their solutions. With the results and discussions it presents, Periodicities in Nonlinear Difference Equations places a few more stones in the foundation of the basic theory of nonlinear difference equations. Researchers and graduate students working in difference equations and discrete dynamical systems will find much to intrigue them and inspire further work in this area.

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