Stability, Instability and Chaos

An Introduction to the Theory of Nonlinear Differential Equations

Author: Paul Glendinning

Publisher: Cambridge University Press

ISBN:

Category: Mathematics

Page: 388

View: 353

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:

Category: Mathematics

Page: 104

View: 132

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

Publisher: Walter de Gruyter

ISBN:

Category: Mathematics

Page: 244

View: 913

In recent years, there has been a tremendous amount of research activity in the general area of population dynamics, particularly the Lotka-Volterra system, which has been a rich source of mathematical ideas from both theoretical and application points of view. In spite of the technological advances, many authors seem to be unaware of the bulk of the work that has been done in this area recently. This often leads to duplication of work and frustration to the authors as well as to the editors of various journals. This book is built out of lecture notes and consists of three chapters written by four mathematicians with overlapping expertise that cover a broad sector of the research in this area. Each chapter consists of carefully written introductory exposition, main breakthroughs, open questions and bibliographies. The chapters present recent developments on topics involving the dynamic behavior of solutions and topics such as stability theory, permanence, persistence, extinction, existence of positive solutions for the Lotka-Volterra and related systems. This fills a void in the literature, by making available a source book of relevant information on the theory, methods and applications of an important area of research.

Nonlinear Dynamics, Volume 1

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

Author: Gaëtan Kerschen

Publisher: Springer

ISBN:

Category: Technology & Engineering

Page: 531

View: 267

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:

Category: Technology & Engineering

Page: 483

View: 920

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.

Mathematics Today

Bulletin of the Institute of Mathematics and Its Applications

Author:

Publisher:

ISBN:

Category: Mathematics

Page:

View: 440

AIAA Journal

Author: American Institute of Aeronautics and Astronautics

Publisher:

ISBN:

Category: Aeronautics

Page:

View: 615

Proceedings

Biological sciences

Author:

Publisher:

ISBN:

Category: Biology

Page:

View: 856

Nonlinear Systems

Author: P. G. Drazin

Publisher: Cambridge University Press

ISBN:

Category: Mathematics

Page: 317

View: 164

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.