Stability, Instability and Chaos

An Introduction to the Theory of Nonlinear Differential Equations

Author: Paul Glendinning

Publisher: Cambridge University Press

ISBN: 9780521425667

Category: Mathematics

Page: 388

View: 2806

An introduction to nonlinear differential equations which equips undergraduate students with the know-how to appreciate stability theory and bifurcation.

Chaotic Dynamics in Nonlinear Theory

Author: Lakshmi Burra

Publisher: Springer

ISBN: 8132220927

Category: Mathematics

Page: 104

View: 7390

Using phase–plane analysis, findings from the theory of topological horseshoes and linked-twist maps, this book presents a novel method to prove the existence of chaotic dynamics. In dynamical systems, complex behavior in a map can be indicated by showing the existence of a Smale-horseshoe-like structure, either for the map itself or its iterates. This usually requires some assumptions about the map, such as a diffeomorphism and some hyperbolicity conditions. In this text, less stringent definitions of a horseshoe have been suggested so as to reproduce some geometrical features typical of the Smale horseshoe, while leaving out the hyperbolicity conditions associated with it. This leads to the study of the so-called topological horseshoes. The presence of chaos-like dynamics in a vertically driven planar pendulum, a pendulum of variable length, and in other more general related equations is also proved.

Lotka-Volterra and Related Systems

Recent Developments in Population Dynamics

Author: Shair Ahmad,Ivanka M. Stamova

Publisher: Walter de Gruyter

ISBN: 3110269848

Category: Mathematics

Page: 244

View: 2326

This book facilitates research in the general area of population dynamics by presenting some of the recent developments involving theories, methods and application in this important area of research. The underlying common feature of the studies included in the book is that they are related, either directly or indirectly, to the well-known Lotka-Volterra systems which offer a variety of mathematical concepts from both theoretical and application points of view.

Nonlinear Dynamics, Volume 1

Proceedings of the 33rd IMAC, A Conference and Exposition on Structural Dynamics, 2015

Author: Gaëtan Kerschen

Publisher: Springer

ISBN: 3319152211

Category: Technology & Engineering

Page: 531

View: 1661

Nonlinear Dynamics, Volume 1. Proceedings of the 33rd IMAC, A Conference and Exposition on Balancing Simulation and Testing, 2015, the first volume of ten from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Structural Dynamics, including papers on: Nonlinear Oscillations Nonlinear Simulation Using Harmonic Balance Nonlinear Modal Analysis Nonlinear System Identification Nonlinear Modeling & Simulation Nonlinearity in Practice Nonlinear Systems Round Robin on Nonlinear System Identification.

Chaos in Electronics

Author: M.A. van Wyk,W.-H. Steeb

Publisher: Springer Science & Business Media

ISBN: 9401589216

Category: Technology & Engineering

Page: 483

View: 7730

Many dynamical systems in physics, chemistry and biology exhibit complex be haviour. The apparently random motion of a fluid is the best known example. How ever also vibrating structures, electronic oscillators, magnetic devices,lasers, chemical oscillators, and population kinetics can behave in a complicated manner. One can find irregular oscillations, which is now known as chaotic behaviour. The research field of nonlinear dynamical systems and especially the study of chaotic systems has been hailed as one of the important breaktroughs in science this century. The sim plest realization of a system with chaotic behaviour is an electronic oscillator. The purpose of this book is to provide a comprehensive introduction to the application of chaos theory to electronic systems. The book provides both the theoretical and experimental foundations of this research field. Each electronic circuit is described in detail together with its mathematical model. Controlling chaos of electronic oscilla tors is also included. End of proofs and examples are indicated by •. Inside examples the end of proofs are indicated with O. We wish to express our gratitude to Catharine Thompson for a critical reading of the manuscript. Any useful suggestions and comments are welcome. Email address of the first author: [email protected] TRSA. AC. ZA Email address of the first author: [email protected] RAU. AC. ZA Home page of the authors: http://zeus. rau. ac. za/steeb/steeb. html xi Chapter 1 Introduction 1.

Introduction to Hydrodynamic Stability

Author: P. G. Drazin

Publisher: Cambridge University Press

ISBN: 9780521009652

Category: Science

Page: 258

View: 7640

Introduces instability of flows and their transition to turbulence. Suitable for a graduate course.

An Introduction to Ordinary Differential Equations

Author: James C. Robinson

Publisher: Cambridge University Press

ISBN: 1139450026

Category: Mathematics

Page: N.A

View: 620

This refreshing, introductory textbook covers both standard techniques for solving ordinary differential equations, as well as introducing students to qualitative methods such as phase-plane analysis. The presentation is concise, informal yet rigorous; it can be used either for 1-term or 1-semester courses. Topics such as Euler's method, difference equations, the dynamics of the logistic map, and the Lorenz equations, demonstrate the vitality of the subject, and provide pointers to further study. The author also encourages a graphical approach to the equations and their solutions, and to that end the book is profusely illustrated. The files to produce the figures using MATLAB are all provided in an accompanying website. Numerous worked examples provide motivation for and illustration of key ideas and show how to make the transition from theory to practice. Exercises are also provided to test and extend understanding: solutions for these are available for teachers.

Mathematics Today

Bulletin of the Institute of Mathematics and Its Applications

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 9665

Infinite-Dimensional Dynamical Systems

An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors

Author: James C. Robinson

Publisher: Cambridge University Press

ISBN: 9780521632041

Category: Mathematics

Page: 461

View: 1910

This book develops the theory of global attractors for a class of parabolic PDEs which includes reaction-diffusion equations and the Navier-Stokes equations, two examples that are treated in detail. A lengthy chapter on Sobolev spaces provides the framework that allows a rigorous treatment of existence and uniqueness of solutions for both linear time-independent problems (Poisson's equation) and the nonlinear evolution equations which generate the infinite-dimensional dynamical systems of the title. Attention then switches to the global attractor, a finite-dimensional subset of the infinite-dimensional phase space which determines the asymptotic dynamics. In particular, the concluding chapters investigate in what sense the dynamics restricted to the attractor are themselves 'finite-dimensional'. The book is intended as a didactic text for first year graduates, and assumes only a basic knowledge of Banach and Hilbert spaces, and a working understanding of the Lebesgue integral.

AIAA Journal

Author: American Institute of Aeronautics and Astronautics

Publisher: N.A

ISBN: N.A

Category: Aeronautics

Page: N.A

View: 8453

An Introduction to Stochastic Dynamics

Author: Jinqiao Duan

Publisher: Cambridge University Press

ISBN: 1107075394

Category: Mathematics

Page: 307

View: 4190

An accessible introduction for applied mathematicians to concepts and techniques for describing, quantifying, and understanding dynamics under uncertainty.

Finite Volume Methods for Hyperbolic Problems

Author: Randall J. LeVeque

Publisher: Cambridge University Press

ISBN: 9780521009249

Category: Mathematics

Page: 558

View: 3586

An introduction to hyperbolic PDEs and a class of numerical methods for approximating their solution, including both linear problems and nonlinear conservation laws.

Nonlinear Dynamics

A Two-Way Trip from Physics to Math

Author: H.G Solari,M.A Natiello,G.B Mindlin

Publisher: CRC Press

ISBN: 9780750303804

Category: Science

Page: 366

View: 4008

Nonlinear Dynamics: A Two-Way Trip from Physics to Math provides readers with the mathematical tools of nonlinear dynamics to tackle problems in all areas of physics. The selection of topics emphasizes bifurcation theory and topological analysis of dynamical systems. The book includes real-life problems and experiments as well as exercises and worked examples to test understanding.

Wave Motion

Author: J. Billingham,A. C. King

Publisher: Cambridge University Press

ISBN: 9780521634502

Category: Mathematics

Page: 468

View: 1619

Textbook on wave phenomena for advanced undergraduate courses; worked examples, exercises and solutions for teachers.

Bäcklund and Darboux Transformations

Geometry and Modern Applications in Soliton Theory

Author: C. Rogers,W. K. Schief

Publisher: Cambridge University Press

ISBN: 9780521012881

Category: Mathematics

Page: 413

View: 4426

Explores deep and fascinating connections between a ubiquitous class of physically important waves known as solitons.

The British National Bibliography

Author: Arthur James Wells

Publisher: N.A

ISBN: N.A

Category: English literature

Page: N.A

View: 3260

Proceedings

Biological sciences

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Biology

Page: N.A

View: 2160

A First Course in Continuum Mechanics

Author: Oscar Gonzalez,Andrew M. Stuart

Publisher: Cambridge University Press

ISBN: 0521886805

Category: Science

Page: 394

View: 5543

A concise account of classic theories of fluids and solids, for graduate and advanced undergraduate courses in continuum mechanics.

A First Course in Combinatorial Optimization

Author: Jon Lee

Publisher: Cambridge University Press

ISBN: 9780521010122

Category: Business & Economics

Page: 211

View: 754

A First Course in Combinatorial Optimization is a text for a one-semester introductory graduate-level course for students of operations research, mathematics, and computer science. It is a self-contained treatment of the subject, requiring only some mathematical maturity. Topics include: linear and integer programming, polytopes, matroids and matroid optimization, shortest paths, and network flows. Central to the exposition is the polyhedral viewpoint, which is the key principle underlying the successful integer-programming approach to combinatorial-optimization problems. Another key unifying topic is matroids. The author does not dwell on data structures and implementation details, preferring to focus on the key mathematical ideas that lead to useful models and algorithms. Problems and exercises are included throughout as well as references for further study.