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.
Topics covered include differential equations of the 1st order, the Riccati equation and existence theorems, 2nd order equations, elliptic integrals and functions, nonlinear mechanics, nonlinear integral equations, more. Includes 137 problems.
Since the popularization of chaos theory, great interest has been generated in non-linear dynamical systems. This text presents an introduction to the basic mathematical concepts and techniques needed to describe and analyze these, aimed at students who have taken a first course in calculus. After reviewing the basic ideas of differential equations, matrix algebra and iteration methods, first and second order continuous systems are discussed. Chapter Four investigates discrete systems and the final chapter is a collection of investigations that can be explored as more open ended tasks.
An Introduction to Linear, Sampled & Non-linear Systems
Author: T. Dougherty
Publisher: World Scientific
Category: Technology & Engineering
The primary function of this book is to serve as a textbook on linear systems and control. It is aimed principally at undergraduates taking courses in Electrical Engineering, Electronics or Mechanical Engineering who are in the penultimate and final years of an Honours degree. Because the text is closely integrated with the use of a widely available software package, it will also be of interest and use to a more expert audience with a control background, but who may not be familiar with these invaluable tools. Finally, it may be of use to others who may not be control specialists, but who need to acquire a background of control for other purposes. Some of the material has been used successfully for such a purpose with an M.Sc programme for Power Engineering students.
This textbook provides an introduction to the new science of nonlinear physics for advanced undergraduates, beginning graduate students, and researchers entering the field. The chapters, by pioneers and experts in the field, share a unified perspective. Nonlinear science developed out of the increasing ability to investigate and analyze systems for which effects are not simply linear functions of their causes; it is associated with such well-known code words as chaos, fractals, pattern formation, solitons, cellular automata, and complex systems. Nonlinear phenomena are important in many fields, including dynamical systems, fluid dynamics, materials science, statistical physics, and paritcel physics. The general principles developed in this text are applicable in a wide variety of fields in the natural and social sciences. The book will thus be of interest not only to physicists, but also to engineers, chemists, geologists, biologists, economists, and others interested in nonlinear phenomena. Examples and exercises complement the text, and extensive references provide a guide to research in the field.
This book introduces the key concepts of nonlinear finite element analysis procedures. The book explains the fundamental theories of the field and provides instructions on how to apply the concepts to solving practical engineering problems. Instead of covering many nonlinear problems, the book focuses on three representative problems: nonlinear elasticity, elastoplasticity, and contact problems. The book is written independent of any particular software, but tutorials and examples using four commercial programs are included as appendices: ANSYS, NASTRAN, ABAQUS, and MATLAB. In particular, the MATLAB program includes all source codes so that students can develop their own material models, or different algorithms. Please visit the author's website for supplemental material, including PowerPoint presentations and MATLAB codes, at http://www2.mae.ufl.edu/nkim/INFEM/
Focuses on System Identification applications of the adaptive methods presented. but which can also be applied to other applications of adaptive nonlinear processes. Covers recent research results in the area of adaptive nonlinear system identification from the authors and other researchers in the field.
The text of this edition has been revised to bring it into line with current teaching, including an expansion of the material on bifurcations and chaos. It is directed towards practical applications of the theory with examples and problems.