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.

AIAA Journal

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


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.

Bulletin

Author:
Publisher:
ISBN: UOM:39015046528637
Release Date: 1995
Genre: Mathematics


Nonlinear Systems

Author: P. G. Drazin
Publisher: Cambridge University Press
ISBN: 0521406684
Release Date: 1992-06-26
Genre: Mathematics

A coherent treatment of nonlinear systems covering chaos, fractals, and bifurcation, as well as equilibrium, stability, and nonlinear oscillations. The systems treated are mostly of difference and differential equations. The author introduces the mathematical properties of nonlinear systems as an integrated theory, rather than simply presenting isolated fashionable topics. The topics are discussed in as concrete a way as possible, worked examples and problems are used to motivate and illustrate the general principles. More advanced parts of the text are denoted by asterisks, thus making it ideally suited to both undergraduate and graduate courses.

Proceedings

Author:
Publisher:
ISBN: UOM:39015049389862
Release Date: 1999
Genre: Biology