Stability Instability and Chaos

Author: Paul Glendinning
Publisher: Cambridge University Press
ISBN: 0521425662
Release Date: 1994-11-25
Genre: Mathematics

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: 9788132220923
Release Date: 2014-09-10
Genre: Mathematics

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.

Nonlinear Dynamics Volume 1

Author: Gaëtan Kerschen
Publisher: Springer
ISBN: 9783319152219
Release Date: 2015-08-14
Genre: Technology & Engineering

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
Publisher: Springer Science & Business Media
ISBN: 9789401589215
Release Date: 2013-06-29
Genre: Technology & Engineering

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: 9781316582879
Release Date: 2002-09-09
Genre: Science

Instability of flows and their transition to turbulence are widespread phenomena in engineering and the natural environment, and are important in applied mathematics, astrophysics, biology, geophysics, meteorology, oceanography and physics as well as engineering. This is a textbook to introduce these phenomena at a level suitable for a graduate course, by modelling them mathematically, and describing numerical simulations and laboratory experiments. The visualization of instabilities is emphasized, with many figures, and in references to more still and moving pictures. The relation of chaos to transition is discussed at length. Many worked examples and exercises for students illustrate the ideas of the text. Readers are assumed to be fluent in linear algebra, advanced calculus, elementary theory of ordinary differential equations, complex variables and the elements of fluid mechanics. The book is aimed at graduate students but will also be very useful for specialists in other fields.

Nonlinear Oscillations Dynamical Systems and Bifurcations of Vector Fields

Author: John Guckenheimer
Publisher: Springer Science & Business Media
ISBN: 9781461211402
Release Date: 2013-11-21
Genre: Mathematics

An application of the techniques of dynamical systems and bifurcation theories to the study of nonlinear oscillations. Taking their cue from Poincare, the authors stress the geometrical and topological properties of solutions of differential equations and iterated maps. Numerous exercises, some of which require nontrivial algebraic manipulations and computer work, convey the important analytical underpinnings of problems in dynamical systems and help readers develop an intuitive feel for the properties involved.

Introduction to Symmetry Analysis Paperback with CD ROM

Author: Brian Cantwell
Publisher: Cambridge University Press
ISBN: 0521777402
Release Date: 2002-09-23
Genre: Mathematics

Symmetry analysis based on Lie group theory is the most important method for solving nonlinear problems aside from numerical computation. The method can be used to find the symmetries of almost any system of differential equations and the knowledge of these symmetries can be used to reduce the complexity of physical problems governed by the equations. This is a broad, self-contained, introduction to the basics of symmetry analysis for first and second year graduate students in science, engineering and applied mathematics. Mathematica-based software for finding the Lie point symmetries and Lie-Bäcklund symmetries of differential equations is included on a CD along with more than forty sample notebooks illustrating applications ranging from simple, low order, ordinary differential equations to complex systems of partial differential equations. MathReader 4.0 is included to let the user read the sample notebooks and follow the procedure used to find symmetries.

AIAA Journal

Author: American Institute of Aeronautics and Astronautics
ISBN: STANFORD:36105113188309
Release Date: 2003
Genre: Aeronautics

Linear Elastic Waves

Author: John G. Harris
Publisher: Cambridge University Press
ISBN: 052164383X
Release Date: 2001-08-06
Genre: Mathematics

An advanced level textbook on wave propagation and scattering directed at applied mathematicians, seismologists, and engineers.

Introduction to Applied Nonlinear Dynamical Systems and Chaos

Author: Stephen Wiggins
Publisher: Springer Science & Business Media
ISBN: 9781475740677
Release Date: 2013-03-09
Genre: Mathematics

This volume is an introduction to applied nonlinear dynamics and chaos. The emphasis is on teaching the techniques and ideas that will enable students to take specific dynamical systems and obtain some quantitative information about their behavior. The new edition has been updated and extended throughout, and contains an extensive bibliography and a detailed glossary of terms.

Nonlinear Dynamics

Author: H.G Solari
Publisher: CRC Press
ISBN: 0750303808
Release Date: 1996-01-01
Genre: Science

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.

Ordinary Differential Equations with Applications

Author: Carmen Chicone
Publisher: Springer Science & Business Media
ISBN: 9780387357942
Release Date: 2006-09-23
Genre: Mathematics

Based on a one-year course taught by the author to graduates at the University of Missouri, this book provides a student-friendly account of some of the standard topics encountered in an introductory course of ordinary differential equations. In a second semester, these ideas can be expanded by introducing more advanced concepts and applications. A central theme in the book is the use of Implicit Function Theorem, while the latter sections of the book introduce the basic ideas of perturbation theory as applications of this Theorem. The book also contains material differing from standard treatments, for example, the Fiber Contraction Principle is used to prove the smoothness of functions that are obtained as fixed points of contractions. The ideas introduced in this section can be extended to infinite dimensions.

Finite Volume Methods for Hyperbolic Problems

Author: Randall J. LeVeque
Publisher: Cambridge University Press
ISBN: 9781139434188
Release Date: 2002-08-26
Genre: Mathematics

This book, first published in 2002, contains an introduction to hyperbolic partial differential equations and a powerful class of numerical methods for approximating their solution, including both linear problems and nonlinear conservation laws. These equations describe a wide range of wave propagation and transport phenomena arising in nearly every scientific and engineering discipline. Several applications are described in a self-contained manner, along with much of the mathematical theory of hyperbolic problems. High-resolution versions of Godunov's method are developed, in which Riemann problems are solved to determine the local wave structure and limiters are then applied to eliminate numerical oscillations. These methods were originally designed to capture shock waves accurately, but are also useful tools for studying linear wave-propagation problems, particularly in heterogenous material. The methods studied are implemented in the CLAWPACK software package and source code for all the examples presented can be found on the web, along with animations of many of the simulations. This provides an excellent learning environment for understanding wave propagation phenomena and finite volume methods.