Global Behavior of Some Nonlinear Difference Equations PDF Download
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Author: Mihaela O. Predescu
Publisher:
ISBN:
Category : Nonlinear difference equations
Languages : en
Pages : 190
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Author: Mihaela O. Predescu
Publisher:
ISBN:
Category : Nonlinear difference equations
Languages : en
Pages : 190
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Book Description
Author: Carol B. Overdeep
Publisher:
ISBN:
Category : Nonlinear difference equations
Languages : en
Pages : 156
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Book Description
Author: V.L. Kocic
Publisher: Springer Science & Business Media
ISBN: 9401717036
Category : Mathematics
Languages : en
Pages : 237
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Book Description
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:
ISBN:
Category : Nonlinear difference equations
Languages : en
Pages : 144
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Author: E.A. Grove
Publisher: CRC Press
ISBN: 0849331560
Category : Mathematics
Languages : en
Pages : 395
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Book Description
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: Hamdy Elmetwally
Publisher: LAP Lambert Academic Publishing
ISBN: 9783843375672
Category :
Languages : en
Pages : 108
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Book Description
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: H. Sedaghat
Publisher: Springer Science & Business Media
ISBN: 9401704171
Category : Mathematics
Languages : en
Pages : 396
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Book Description
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: Mustafa R.S. Kulenovic
Publisher: Chapman and Hall/CRC
ISBN: 9781584882756
Category : Mathematics
Languages : en
Pages : 232
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Book Description
This self-contained monograph provides systematic, instructive analysis of second-order rational difference equations. After classifying the various types of these equations and introducing some preliminary results, the authors systematically investigate each equation for semicycles, invariant intervals, boundedness, periodicity, and global stability. Of paramount importance in their own right, the results presented also offer prototypes towards the development of the basic theory of the global behavior of solutions of nonlinear difference equations of order greater than one. The techniques and results in this monograph are also extremely useful in analyzing the equations in the mathematical models of various biological systems and other applications. Each chapter contains a section of open problems and conjectures that will stimulate further research interest in working towards a complete understanding of the dynamics of the equation and its functional generalizations-many of them ideal for research projects or Ph.D. theses. Clear, simple, and direct exposition combined with thoughtful uniformity in the presentation make Dynamics of Second Order Rational Difference Equations valuable as an advanced undergraduate or a graduate-level text, a reference for researchers, and as a supplement to every textbook on difference equations at all levels of instruction.
Author: Linda J. S. Allen
Publisher: World Scientific Publishing Company Incorporated
ISBN: 9789812565204
Category : Mathematics
Languages : en
Pages : 324
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Book Description
A discrete-time Beverton-Holt competition model / Azmy S. Ackleh, Youssef M. Dib and Sophia R.-J. Jang -- A dynamic analysis of the Bush fiscal policy / Richard H. Day and Chengyu Yang -- A hybrid approximation to certain delay differential equation with a constant delay / George Seifert -- Compulsory asymptotic behavior of solutions of two-dimensional systems of difference equations / Josef Diblík and Irena R°uz̮ic̮ková -- Discrete models of differential equations : the roles of dynamic consistency and positivity / Ronald E. Mickens -- Enveloping implies global stability / Paul Cull -- Global asymptotic stability in the Jia Li model for genetically altered mosquitoes / Robert J. Sacker and Hubertus F. von Bremen -- Global behavior of solutions of a nonlinear second-order nonautonomous difference equation / Vlajko L. Kocic -- How can three species coexist in a periodic chemostat? Mathematical and numerical study / Shinji Nakaoka and Yasuhiro Takeuchi -- Information-theoretic measures of discrete orthogonal polynomials / Jesus Sanchez Dehesa ... [et al.] -- Local approximation of invariant fiber bundles : an algorithmic approach / Christian Pötzsche and Martin Rasmussen -- Necessary and sufficient conditions for oscillation of coupled nonlinear discrete systems / Serena Matucci and Pavel R̮ehák -- Non-standard finite difference methods for dissipative singular perturbation problems / Jean M.-S. Lubuma and Kailash C. Patidar -- On a class of generalized autoregressive processes / Kamal C. Chanda -- On [symbol] with period-two coefficients / Carol H. Gibbons and Carol B. Overdeep -- Periodically forced nonlinear difference equations with delay / Abdul-Aziz Yakubu -- Regularity of difference equations / Jarmo Hietarinta -- Robustness in difference equations / Jack K. Hale -- Solvability of the discrete LQR-problem under minimal assumptions / Roman Hilscher and Vera Zeidan -- Some discrete competition models and the principle of competitive exclusion / Jim M. Cushing and Sheree Le Varge -- Stability under constantly acting perturbations for difference equations and averaging / Vladimir Burd -- Symbolic dynamics in the study of bursting electrical activity / Jorge Duarte, Jose Sousa Ramos and Luis Silva
Author: Candace M. Kent
Publisher:
ISBN: 9783110483024
Category :
Languages : en
Pages :
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