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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.

Nonlinear Partial Differential Equations with Applications

2006-01-17 Mathematics
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Release : 2006-01-17
Genre : Mathematics
Kind : eBook
Book Rating : 970/5 ( reviews)

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Book Synopsis Nonlinear Partial Differential Equations with Applications by : Tomás Roubicek

Download or read book Nonlinear Partial Differential Equations with Applications written by Tomás Roubicek. This book was released on 2006-01-17. Available in PDF, EPUB and Kindle. Book excerpt: This book primarily concerns quasilinear and semilinear elliptic and parabolic partial differential equations, inequalities, and systems. The exposition quickly leads general theory to analysis of concrete equations, which have specific applications in such areas as electrically (semi-) conductive media, modeling of biological systems, and mechanical engineering. Methods of Galerkin or of Rothe are exposed in a large generality.

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
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

Nonlinear Differential Equations and Dynamical Systems

2021-04-15 Mathematics
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Release : 2021-04-15
Genre : Mathematics
Kind : eBook
Book Rating : 108/5 ( reviews)

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Book Synopsis Nonlinear Differential Equations and Dynamical Systems by : Feliz Manuel Minhós

Download or read book Nonlinear Differential Equations and Dynamical Systems written by Feliz Manuel Minhós. This book was released on 2021-04-15. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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