Global Behavior Of Nonlinear Difference Equations Of Higher Order With Applications
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Author | : V.L. Kocic |
Publisher | : Springer Science & Business Media |
Total Pages | : 237 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 9401717036 |
Download Global Behavior of Nonlinear Difference Equations of Higher Order with Applications Book in PDF, Epub and Kindle
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.
Author | : Cathy Ann Clark |
Publisher | : |
Total Pages | : 144 |
Release | : 2004 |
Genre | : Nonlinear difference equations |
ISBN | : |
Download Global Behavior of Nonlinear Difference Equations Book in PDF, Epub and Kindle
Author | : Mihaela O. Predescu |
Publisher | : |
Total Pages | : 190 |
Release | : 2003 |
Genre | : Nonlinear difference equations |
ISBN | : |
Download Global Behavior of Some Nonlinear Difference Equations Book in PDF, Epub and Kindle
Author | : H. Sedaghat |
Publisher | : Springer Science & Business Media |
Total Pages | : 396 |
Release | : 2013-03-14 |
Genre | : Mathematics |
ISBN | : 9401704171 |
Download Nonlinear Difference Equations Book in PDF, Epub and Kindle
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.
Author | : E.A. Grove |
Publisher | : CRC Press |
Total Pages | : 395 |
Release | : 2004-12-16 |
Genre | : Mathematics |
ISBN | : 0849331560 |
Download Periodicities in Nonlinear Difference Equations Book in PDF, Epub and Kindle
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.
Author | : Carol B. Overdeep |
Publisher | : |
Total Pages | : 156 |
Release | : 2003 |
Genre | : Nonlinear difference equations |
ISBN | : |
Download Global Behavior of Some Nonlinear Difference Equations Book in PDF, Epub and Kindle
Author | : Hamdy Elmetwally |
Publisher | : LAP Lambert Academic Publishing |
Total Pages | : 108 |
Release | : 2010-11 |
Genre | : |
ISBN | : 9783843375672 |
Download Qualitative Study of Nonlinear Difference Equations Book in PDF, Epub and Kindle
We establish a global convergence result for the higher order difference equation where k is a positive integer and are positive initial conditions and then apply this result to show that, under appropriate hypotheses, every positive solution of the difference equation, converges to a period p solution, where the period p is easily determined in terms of the coefficients. Also we present some known results and derive several new ones on the boundedness and the global stability of the solutions of the difference equation We study the global stability, the boundedness nature, and the periodic character of the positive solutions of the difference equation which is interesting in its own right, but which may also be viewed as describing a population model. We obtain some sufficient conditions for the existence of the solutions and the asymptotic behavior of both linear and nonlinear system of differential equations with continuous coefficients and piecewise constant argument of the form.
Author | : Saber Elaydi |
Publisher | : Springer Science & Business Media |
Total Pages | : 547 |
Release | : 2005-03-29 |
Genre | : Mathematics |
ISBN | : 0387230599 |
Download An Introduction to Difference Equations Book in PDF, Epub and Kindle
A must-read for mathematicians, scientists and engineers who want to understand difference equations and discrete dynamics Contains the most complete and comprehenive analysis of the stability of one-dimensional maps or first order difference equations. Has an extensive number of applications in a variety of fields from neural network to host-parasitoid systems. Includes chapters on continued fractions, orthogonal polynomials and asymptotics. Lucid and transparent writing style
Author | : Candace M. Kent |
Publisher | : |
Total Pages | : |
Release | : 2018 |
Genre | : |
ISBN | : 9783110483024 |
Download Nonlinear Nonautonomous Difference Equations Book in PDF, Epub and Kindle
Author | : Feliz Manuel Minhós |
Publisher | : MDPI |
Total Pages | : 158 |
Release | : 2021-04-15 |
Genre | : Mathematics |
ISBN | : 3036507108 |
Download Nonlinear Differential Equations and Dynamical Systems Book in PDF, Epub and Kindle
This Special Edition contains new results on Differential and Integral Equations and Systems, covering higher-order Initial and Boundary Value Problems, fractional differential and integral equations and applications, non-local optimal control, inverse, and higher-order nonlinear boundary value problems, distributional solutions in the form of a finite series of the Dirac delta function and its derivatives, asymptotic properties’ oscillatory theory for neutral nonlinear differential equations, the existence of extremal solutions via monotone iterative techniques, predator–prey interaction via fractional-order models, among others. Our main goal is not only to show new trends in this field but also to showcase and provide new methods and techniques that can lead to future research.