Periodicities In Nonlinear Difference Equations

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Periodicities in Nonlinear Difference Equations

E.A. Grove,G. Ladas
Periodicities in Nonlinear Difference Equations Book PDF

Author : E.A. Grove,G. Ladas
Publisher : CRC Press
Page : 395 pages
File Size : 48,7 Mb
Release : 2004-12-16
Category : Mathematics
ISBN : 9780849331565

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Periodicities in Nonlinear Difference Equations by E.A. Grove,G. Ladas Pdf

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

V.L. Kocic,G. Ladas
Global Behavior of Nonlinear Difference Equations of Higher Order with Applications Book PDF

Author : V.L. Kocic,G. Ladas
Publisher : Springer Science & Business Media
Page : 256 pages
File Size : 55,5 Mb
Release : 1993-05-31
Category : Mathematics
ISBN : 079232286X

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Global Behavior of Nonlinear Difference Equations of Higher Order with Applications by V.L. Kocic,G. Ladas Pdf

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.

Difference Equations, Discrete Dynamical Systems and Applications

Lluís Alsedà i Soler,Jim M. Cushing,Saber Elaydi,Alberto A. Pinto
Difference Equations Discrete Dynamical Systems and Applications Book PDF

Author : Lluís Alsedà i Soler,Jim M. Cushing,Saber Elaydi,Alberto A. Pinto
Publisher : Springer
Page : 335 pages
File Size : 44,9 Mb
Release : 2016-10-22
Category : Mathematics
ISBN : 9783662529270

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Difference Equations, Discrete Dynamical Systems and Applications by Lluís Alsedà i Soler,Jim M. Cushing,Saber Elaydi,Alberto A. Pinto Pdf

These proceedings of the 18th International Conference on Difference Equations and Applications cover a number of different aspects of difference equations and discrete dynamical systems, as well as the interplay between difference equations and dynamical systems. The conference was organized by the Department of Mathematics at the Universitat Autònoma de Barcelona (UAB) under the auspices of the International Society of Difference Equations (ISDE) and held in Barcelona (Catalonia, Spain) in July 2012. Its purpose was to bring together experts and novices in these fields to discuss the latest developments. The book gathers contributions in the field of combinatorial and topological dynamics, complex dynamics, applications of difference equations to biology, chaotic linear dynamics, economic dynamics and control and asymptotic behavior, and periodicity of difference equations. As such it is of interest to researchers and scientists engaged in the theory and applications of difference equations and discrete dynamical systems.

Difference Equations For Scientists And Engineering: Interdisciplinary Difference Equations

Michael A Radin
Difference Equations For Scientists And Engineering Interdisciplinary Difference Equations Book PDF

Author : Michael A Radin
Publisher : World Scientific
Page : 330 pages
File Size : 48,5 Mb
Release : 2019-09-24
Category : Mathematics
ISBN : 9789811202988

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Difference Equations For Scientists And Engineering: Interdisciplinary Difference Equations by Michael A Radin Pdf

'Radlin has done a nice job in producing a textbook which provides a learner friendly introduction to difference equations. It would suit as a core text for a first year course in the topic, aimed, as the title suggests, at physical science or engineering undergraduates. The student who is prepared to work through the book will get a good grounding in basic techniques and gain a feel for the possible behaviours of standard equations. He will also be given some indication of the usefulness and potential complexity of discrete systems in modern science and engineering.'London Mathematical SocietyWe introduce interdisciplinary research and get students and the audience familiarized with the difference equations; solving them explicitly, determining the long-term behavior of solutions (convergence, boundedness and periodicity). We help to develop intuition in analyzing convergence of solutions in terms of subsequences and analyzing patterns of periodic cycles. Our book helps you learn applications in biology, economics and business, computer science and engineering.

Handbook of Dynamic System Modeling

Paul A. Fishwick
Handbook of Dynamic System Modeling Book PDF

Author : Paul A. Fishwick
Publisher : CRC Press
Page : 760 pages
File Size : 47,7 Mb
Release : 2007-06-01
Category : Mathematics
ISBN : 1420010859

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Handbook of Dynamic System Modeling by Paul A. Fishwick Pdf

The topic of dynamic models tends to be splintered across various disciplines, making it difficult to uniformly study the subject. Moreover, the models have a variety of representations, from traditional mathematical notations to diagrammatic and immersive depictions. Collecting all of these expressions of dynamic models, the Handbook of Dynamic System Modeling explores a panoply of different types of modeling methods available for dynamical systems. Featuring an interdisciplinary, balanced approach, the handbook focuses on both generalized dynamic knowledge and specific models. It first introduces the general concepts, representations, and philosophy of dynamic models, followed by a section on modeling methodologies that explains how to portray designed models on a computer. After addressing scale, heterogeneity, and composition issues, the book covers specific model types that are often characterized by specific visual- or text-based grammars. It concludes with case studies that employ two well-known commercial packages to construct, simulate, and analyze dynamic models. A complete guide to the fundamentals, types, and applications of dynamic models, this handbook shows how systems function and are represented over time and space and illustrates how to select a particular model based on a specific area of interest.

Advances in Discrete Dynamical Systems, Difference Equations and Applications

Saber Elaydi,Mustafa R. S. Kulenović,Senada Kalabušić
Advances in Discrete Dynamical Systems Difference Equations and Applications Book PDF

Author : Saber Elaydi,Mustafa R. S. Kulenović,Senada Kalabušić
Publisher : Springer Nature
Page : 534 pages
File Size : 45,8 Mb
Release : 2023-03-25
Category : Mathematics
ISBN : 9783031252259

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Advances in Discrete Dynamical Systems, Difference Equations and Applications by Saber Elaydi,Mustafa R. S. Kulenović,Senada Kalabušić Pdf

​This book comprises selected papers of the 26th International Conference on Difference Equations and Applications, ICDEA 2021, held virtually at the University of Sarajevo, Bosnia and Herzegovina, in July 2021. The book includes the latest and significant research and achievements in difference equations, discrete dynamical systems, and their applications in various scientific disciplines. The book is interesting for Ph.D. students and researchers who want to keep up to date with the latest research, developments, and achievements in difference equations, discrete dynamical systems, and their applications, the real-world problems.

An Introduction to Difference Equations

Saber Elaydi
An Introduction to Difference Equations Book PDF

Author : Saber Elaydi
Publisher : Springer Science & Business Media
Page : 547 pages
File Size : 42,5 Mb
Release : 2005-03-29
Category : Mathematics
ISBN : 9780387230597

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An Introduction to Difference Equations by Saber Elaydi Pdf

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

Dynamics, Games and Science I

Mauricio Matos Peixoto,Alberto Adrego Pinto,David A. Rand
Dynamics Games and Science I Book PDF

Author : Mauricio Matos Peixoto,Alberto Adrego Pinto,David A. Rand
Publisher : Springer Science & Business Media
Page : 809 pages
File Size : 48,5 Mb
Release : 2011-03-29
Category : Mathematics
ISBN : 9783642114564

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Dynamics, Games and Science I by Mauricio Matos Peixoto,Alberto Adrego Pinto,David A. Rand Pdf

Dynamics, Games and Science I and II are a selection of surveys and research articles written by leading researchers in mathematics. The majority of the contributions are on dynamical systems and game theory, focusing either on fundamental and theoretical developments or on applications to modeling in biology, ecomonics, engineering, finances and psychology. The papers are based on talks given at the International Conference DYNA 2008, held in honor of Mauricio Peixoto and David Rand at the University of Braga, Portugal, on September 8-12, 2008. The aim of these volumes is to present cutting-edge research in these areas to encourage graduate students and researchers in mathematics and other fields to develop them further.

Discrete Dynamics and Difference Equations

Saber N. Elaydi,Henrique Oliveira,Jose Manuel Ferreira
Discrete Dynamics and Difference Equations Book PDF

Author : Saber N. Elaydi,Henrique Oliveira,Jose Manuel Ferreira
Publisher : World Scientific
Page : 438 pages
File Size : 46,6 Mb
Release : 2010
Category : Mathematics
ISBN : 9789814287647

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Discrete Dynamics and Difference Equations by Saber N. Elaydi,Henrique Oliveira,Jose Manuel Ferreira Pdf

This volume holds a collection of articles based on the talks presented at ICDEA 2007 in Lisbon, Portugal. The volume encompasses current topics on stability and bifurcation, chaos, mathematical biology, iteration theory, nonautonomous systems, and stochastic dynamical systems.

Form Symmetries and Reduction of Order in Difference Equations

Hassan Sedaghat
Form Symmetries and Reduction of Order in Difference Equations Book PDF

Author : Hassan Sedaghat
Publisher : CRC Press
Page : 327 pages
File Size : 46,6 Mb
Release : 2011-05-24
Category : Mathematics
ISBN : 9781439807606

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Form Symmetries and Reduction of Order in Difference Equations by Hassan Sedaghat Pdf

Form Symmetries and Reduction of Order in Difference Equations presents a new approach to the formulation and analysis of difference equations in which the underlying space is typically an algebraic group. In some problems and applications, an additional algebraic or topological structure is assumed in order to define equations and obtain significant results about them. Reflecting the author’s past research experience, the majority of examples involve equations in finite dimensional Euclidean spaces. The book first introduces difference equations on groups, building a foundation for later chapters and illustrating the wide variety of possible formulations and interpretations of difference equations that occur in concrete contexts. The author then proposes a systematic method of decomposition for recursive difference equations that uses a semiconjugate relation between maps. Focusing on large classes of difference equations, he shows how to find the semiconjugate relations and accompanying factorizations of two difference equations with strictly lower orders. The final chapter goes beyond semiconjugacy by extending the fundamental ideas based on form symmetries to nonrecursive difference equations. With numerous examples and exercises, this book is an ideal introduction to an exciting new domain in the area of difference equations. It takes a fresh and all-inclusive look at difference equations and develops a systematic procedure for examining how these equations are constructed and solved.

Advances in Difference Equations and Discrete Dynamical Systems

Saber Elaydi,Yoshihiro Hamaya,Hideaki Matsunaga,Christian Pötzsche
Advances in Difference Equations and Discrete Dynamical Systems Book PDF

Author : Saber Elaydi,Yoshihiro Hamaya,Hideaki Matsunaga,Christian Pötzsche
Publisher : Springer
Page : 282 pages
File Size : 44,7 Mb
Release : 2017-11-13
Category : Mathematics
ISBN : 9789811064098

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Advances in Difference Equations and Discrete Dynamical Systems by Saber Elaydi,Yoshihiro Hamaya,Hideaki Matsunaga,Christian Pötzsche Pdf

This volume contains the proceedings of the 22nd International Conference on Difference Equations and Applications, held at Osaka Prefecture University, Osaka, Japan, in July 2016. The conference brought together both experts and novices in the theory and applications of difference equations and discrete dynamical systems. The volume features papers in difference equations and discrete dynamical systems with applications to mathematical sciences and, in particular, mathematical biology and economics. This book will appeal to researchers, scientists, and educators who work in the fields of difference equations, discrete dynamical systems, and their applications.

Dynamics of Third-Order Rational Difference Equations with Open Problems and Conjectures

Elias Camouzis,G. Ladas
Dynamics of Third Order Rational Difference Equations with Open Problems and Conjectures Book PDF

Author : Elias Camouzis,G. Ladas
Publisher : CRC Press
Page : 576 pages
File Size : 50,9 Mb
Release : 2007-11-16
Category : Mathematics
ISBN : 1584887664

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Dynamics of Third-Order Rational Difference Equations with Open Problems and Conjectures by Elias Camouzis,G. Ladas Pdf

Extending and generalizing the results of rational equations, Dynamics of Third Order Rational Difference Equations with Open Problems and Conjectures focuses on the boundedness nature of solutions, the global stability of equilibrium points, the periodic character of solutions, and the convergence to periodic solutions, including their periodic trichotomies. The book also provides numerous thought-provoking open problems and conjectures on the boundedness character, global stability, and periodic behavior of solutions of rational difference equations. After introducing several basic definitions and general results, the authors examine 135 special cases of rational difference equations that have only bounded solutions and the equations that have unbounded solutions in some range of their parameters. They then explore the seven known nonlinear periodic trichotomies of third order rational difference equations. The main part of the book presents the known results of each of the 225 special cases of third order rational difference equations. In addition, the appendices supply tables that feature important information on these cases as well as on the boundedness character of all fourth order rational difference equations. A Framework for Future Research The theory and techniques developed in this book to understand the dynamics of rational difference equations will be useful in analyzing the equations in any mathematical model that involves difference equations. Moreover, the stimulating conjectures will promote future investigations in this fascinating, yet surprisingly little known area of research.