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Periodicities in Nonlinear Difference Equations

2004-12-16 Mathematics
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Release : 2004-12-16
Genre : Mathematics
Kind : eBook
Book Rating : 722/5 ( 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

Periodicities in Nonlinear Difference Equations

2004-12-16 Mathematics
Download Periodicities in Nonlinear Difference Equations PDF Online Free

Author :
Release : 2004-12-16
Genre : Mathematics
Kind : eBook
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.

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.

Non-Linear Differential Equations

2016-06-06 Mathematics
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Release : 2016-06-06
Genre : Mathematics
Kind : eBook
Book Rating : 969/5 ( reviews)

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Book Synopsis Non-Linear Differential Equations by : G. Sansone

Download or read book Non-Linear Differential Equations written by G. Sansone. This book was released on 2016-06-06. Available in PDF, EPUB and Kindle. Book excerpt: International Series of Monographs in Pure and Applied Mathematics, Volume 67: Non-Linear Differential Equations, Revised Edition focuses on the analysis of the phase portrait of two-dimensional autonomous systems; qualitative methods used in finding periodic solutions in periodic systems; and study of asymptotic properties. The book first discusses general theorems about solutions of differential systems. Periodic solutions, autonomous systems, and integral curves are explained. The text explains the singularities of Briot-Bouquet theory. The selection takes a look at plane autonomous systems. Topics include limiting sets, plane cycles, isolated singular points, index, and the torus as phase space. The text also examines autonomous plane systems with perturbations and autonomous and non-autonomous systems with one degree of freedom. The book also tackles linear systems. Reducible systems, periodic solutions, and linear periodic systems are considered. The book is a vital source of information for readers interested in applied mathematics.

Nonlinear Ordinary Differential Equations

1991-03-06 Mathematics
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Release : 1991-03-06
Genre : Mathematics
Kind : eBook
Book Rating : 077/5 ( reviews)

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Book Synopsis Nonlinear Ordinary Differential Equations by : R. Grimshaw

Download or read book Nonlinear Ordinary Differential Equations written by R. Grimshaw. This book was released on 1991-03-06. Available in PDF, EPUB and Kindle. Book excerpt: Ordinary differential equations have long been an important area of study because of their wide application in physics, engineering, biology, chemistry, ecology, and economics. Based on a series of lectures given at the Universities of Melbourne and New South Wales in Australia, Nonlinear Ordinary Differential Equations takes the reader from basic elementary notions to the point where the exciting and fascinating developments in the theory of nonlinear differential equations can be understood and appreciated. Each chapter is self-contained, and includes a selection of problems together with some detailed workings within the main text. Nonlinear Ordinary Differential Equations helps develop an understanding of the subtle and sometimes unexpected properties of nonlinear systems and simultaneously introduces practical analytical techniques to analyze nonlinear phenomena. This excellent book gives a structured, systematic, and rigorous development of the basic theory from elementary concepts to a point where readers can utilize ideas in nonlinear differential equations.

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