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Published
**1993** by Springer Netherlands in Dordrecht .

Written in English

Read online- Mathematics,
- Functional equations,
- Systems theory

This volume presents a systematic study of the global behaviour of solutions of nonlinear scalar difference equations of order greater than one. Of particular interest are aspects such as global asymptotic stability, periodicity, permanence and persistence, and also semicycles of solutions. As well as exposing the reader to the very frontiers of the subject, important open problems are also formulated. The book has six chapters. Chapter 1 presents an introduction to the subject and deals with preliminaries. Chapter 2 considers global stability results. Chapter 3 is devoted to rational recursive structures. Chapter 4 describes various applications. The topic of Chapter 5 is periodic cycles, and Chapter 6 discusses a number of open problems and conjectures involving interesting types of difference equations. Each chapter includes notes and references. The volume concludes with three appendices, a comprehensive bibliography, and name and subject indices. For graduate students and researchers whose work involves difference and differential equations.

**Edition Notes**

Statement | by V. L. Kocic, G. Ladas |

Series | Mathematics and Its Applications -- 256, Mathematics and Its Applications -- 256 |

Contributions | Ladas, G. |

Classifications | |
---|---|

LC Classifications | QA431 |

The Physical Object | |

Format | [electronic resource] / |

Pagination | 1 online resource (xi, 228 p.) |

Number of Pages | 228 |

ID Numbers | |

Open Library | OL27041426M |

ISBN 10 | 9048142733, 9401717036 |

ISBN 10 | 9789048142736, 9789401717038 |

OCLC/WorldCa | 851393175 |

**Download Global Behavior of Nonlinear Difference Equations of Higher Order with Applications**

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.

About this book. Introduction. 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).

Book reviews. GLOBAL BEHAVIOR OF NONLINEAR DIFFERENCE EQUATIONS OF HIGHER ORDER WITH APPLICATIONS (Mathematics and its Applications ) Robert M.

May. Search for more papers by this author. Robert M. May. Search for more papers by this author. First published: November Cited by: By V.

Kocic and G. Ladas: pp., US$, ISBN 0 X (Kluwer, ).Cited by: Global Behavior of Nonlinear Difference Equations of Higher Order with Applications by V.L. Kocic and G. Ladas Department of Mathematics, University of Rhode Island. Some nonlinear difference equations, especially second order nonlinear difference equa- tions have been considered by many authors, see [2,3,5–7] and references cited therein.

In these articles, the global attractivity, invariant interval, oscillation, permanence and some other properties of the equations were by: 8. Global behavior of a higher order nonlinear difference equation Article in Journal of Mathematical Analysis and Applications (1) November with 24 Reads How we measure 'reads'.

V.L. Kocic, G. LadasGlobal Behavior of Nonlinear Difference Equations of Higher Order with ApplicationsCited by: 6. Kocic, V.L., Ladas, G.: Global Behavior Global Behavior of Nonlinear Difference Equations of Higher Order with Applications book Nonlinear Difference Equations of Higher Order with Applications.

Kluwer Academic Publishers, Dordrecht () zbMATH Google Scholar by: 1. In this paper we obtain a global attractivity result for the positive equilibrium of a nonlinear second-order difference equation of the form xn+1 = f(xn, xn+1), n = 0, 1, ⃛The result applies to.

Kocic and G. Ladas, “Global Behavior of Nonlinear Difference Equations of Higher Order with Applications,” Kluwer Academic Publishers, Dordrecht, has been cited by the following article: TITLE: Periodicity and Solution of Rational Recurrence Relation of Order.

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 Read more. The study of the nonlinear rational difference equations of a higher order is quite challenging and rewarding, and the results about these equations offer prototypes towards the development of the basic theory of the global behavior of nonlinear difference equations of a big order, recently, many researchers have investigated the behavior of Cited by: Our aim in this paper is to investigate the convergence behavior of the positive solutions of a higher order fuzzy difference equation and show that all positive solutions of this equation converge to its unique positive equilibrium under appropriate assumptions.

Furthermore, we give two examples to account for the applicability of the main result of this : Guangwang Su, Taixiang Sun, Bin Qin. Get this from a library. Global Behavior of Nonlinear Difference Equations of Higher Order with Applications.

[V L Kocic; G Ladas] -- This volume presents a systematic study of the global behaviour of solutions of nonlinear scalar difference equations of order greater than one. Of particular interest are aspects such as global.

In this paper, we study a class of the long-time behavior of solutions to initial-boundary value problems for higher order equations with nonlinear source term and strong damping term.

First of all, give some space and marks as well as the basic assumption of stress and nonlinear source term, take the inner product on both sides Author: Guoguang Lin, Ying Jin. Kocić and G. Ladas, Global Behavior of Nonlinear Difference Equations of Higher Order with Applications, vol.

of Mathematics and Its Applications, Kluwer Academic Publishers Group, Dordrecht, The Netherlands, Author: Yuanyuan Liu, Fanwei Meng. [5] V. Kocic and G. Ladas.´ Global behavior of nonlinear difference equations of higher order with applications, volume of Mathematics and its Applications.

Kluwer Academic Publishers Group, Dordrecht, [6] M. Kulenonvic and G. Ladas.´ Dynamics of second order rational difference equations with open problem and conjectures. Motivated by the above studies, our aim in this paper is to investigate the qualitative behavior of positive solutions of the following exponential system of rational difference equations: where the parameters,, and are positive numbers and the initial conditions are arbitrary nonnegative real by: 7.

Differential Equations and Boundary Value Problems: Computing and Modeling, Global Edition, 5th Edition. Henry Edwards, The University of Georgia, Athens. David E. Penney, University of Georgia, Athens.

Linear Equations of Higher Order. Introduction: Second-Order Linear Equations. Find many great new & used options and get the best deals for Mathematics and Its Applications: Global Behavior of Nonlinear Difference Equations of Higher Order with Applications by G.

Ladas and V. Kocic (, Paperback) at the best online prices at. () Global existence and blow-up of solutionsfor a higher-order kirchhoff-type equation with nonlinear dissipation.

Applied Mathematics Letters() Blow-up of solution of an initial boundary value problem for a damped nonlinear hyperbolic by: Long Time Behavior for Some Higher Order Partial Differential Equations. Proceedings of the International Conference on Cybernetics and Informatics, () Global and Blow-Up Solutions for a Class of Nonlinear Parabolic Problems under Robin Boundary by: the Higher Order Nonlinear Rational Difference.

global behavior of nonlinear difference equations of higher order with applications. Provide us 5 mins and also we will certainly reveal you the very best book to€ Global behavior of. Obviously, higher-order rational difference equations and systems of rational equations have also been widely studied but still have many aspects to be investigated.

The reader can find in the following books [ 4 – 6 ], and works cited therein, many results, applications, and open problems on higher-order equations and rational by: In this paper, we study the qualitative behavior of solutions for a general class of difference equations.

The criteria of local and global stability, boundedness and periodicity character (with period 2 k) of the solution are established.

Moreover, by applying our general results on a population model with two age classes, we establish the qualitative behavior of solutions of this model. 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: by: GLOBAL BEHAVIOR OF SOLUTIONS OF NONLINEAR ODES: FIRST ORDER EQUATIONS O.

COSTIN, M. HUANG AND F. FAUVET Abstract. We determine the behavior of the general solution, small or large, of nonlinear ﬁrst order ODEs in a neighborhood of an irregular singular point chosen to be inﬁnity. We show that the solutions can be controlled in a ramiﬁed.

In this paper we study the oscillatory behavior, the boundedness of the solutions, and the global asymptotic stability of the positive equilibrium of the system of two nonlinear difference equationsxn + 1 = A + yn/xn − p,yn + 1 = A + xn/yn − q,n = 0, 1,p, qare positive integers.

First Order Systems of Ordinary Diﬀerential Equations. Let us begin by introducing the basic object of study in discrete dynamics: the initial value problem for a ﬁrst order system of ordinary diﬀerential equations. Many physical applications lead to higher order systems of ordinary diﬀerential equations.

study of these equations is challenging and rewarding and is still in its infancy. We believe that the nonlinear rational difference equations are of paramount importance in their own right.

Furthermore the results about such equations offer prototypes for the development of the basic theory of the global behavior of nonlinear difference equations.

2 First-Order Differential Equations 3 Second-Order Linear Differential Equations 4 Higher-Order Linear Differential Equations 5 Series Solutions of Second-Order Linear Equations 6 The Laplace Transform 7 Systems of First-Order Linear Equations 8 Numerical Methods 9 Nonlinear Differential Equations and.

KdV equation, namely the Benjamin-Ono equation, which requires more nonlinear techniques, such as gauge transforms, in order to obtain a satisfactory existence and wellposedness theory.

In the ﬁfth chapter we return to the semilinear equations (NLS and NLW), and now establish large data global existence for these equations in the defocusing. Abo-Zeid, Global behavior of a higher order difference equation, Math.

Slovaca, $64$ $(4)$ $()$, $$. Global Behavior of Nonlinear Difference Equations of Higher Order with Applications, Kluwer Academic, Dordrecht, $$.Cited by: 1.

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 special cases of third order rational difference equations.

Among nonlinear PDEs, dispersive and wave equations form an important class of equations. These include the nonlinear Schrödinger equation, the nonlinear wave equation, the Korteweg de Vries equation, and the wave maps equation.

This book is an introduction to the methods and results used in the modern analysis (both locally and globally in. V.L. Kocic and G. Ladas, Global behavior of nonlinear difference equations of higher order with applications, Kluwer Academic Publishers, Dordrecht, Cited by: 1.

Elsayed, E.M. () Dynamics and Behavior of a Higher Order Rational Difference Equation. Journal of Nonlinear Sciences and Applications, 9, Elsayed, E.M.

() On the Global Attractivity and the Periodic Character of a Recursive Sequence. Opuscula Mathematica, 30, Author: Elmetwally M.

Elabbasy, Osama Moaaz, Shaimaa Alsaeed. [3] V.L. Kocic, and G. Ladas, Global Behavior of Nonlinear Difference Equations of Higher Order with Applications, Kluwer, Dordrecht, [4] M.R.S. Kulenovic, and G. Ladas, Dynamics of Second Order Difference Equations with Open Problems and Conjectures, Chapman and.

This textbook presents a systematic study of the qualitative and geometric theory of nonlinear differential equations and dynamical systems. Although the main topic of the book is the local and global behavior of nonlinear systems and their bifurcations, a thorough treatment of linear systems is given at the beginning of the text.

As a result, there has been much focus on the existence of periodic solutions of certain classes of these equations and the asymptotic behavior of these periodic solutions. In this dissertation, we study the existence and global attractivity of both periodic and quasiperiodic solutions of two different higher order nonlinear difference equations.V.

L. Kocic and G. Ladas, Global Behavior of Nonlinear Difference Equations of Higher Order with Applications, Kluwer Academic Publishers, Boston, doi: / Cited by: 5.Nonlinear algebraic equations, which are also called polynomial equations, are defined by equating polynomials (of degree greater than one) to zero.

For example, + −. For a single polynomial equation, root-finding algorithms can be used to find solutions to the equation (i.e., sets of values for the variables that satisfy the equation). However, systems of algebraic equations are more.