Harry Dankowicz and Frank Schilder
Computer Science and Engineering 11
This book provides a comprehensive introduction to the mathematical methodology of parameter continuation, the computational analysis of families of solutions to nonlinear mathematical equations. It develops a systematic formalism for constructing abstract representations of continuation problems and for implementing these in an existing computational platform.
Recipes for Continuation
• lends equal importance to theoretical rigor, algorithm development, and software engineering;
• demonstrates the use of fully developed toolbox templates for single- and multisegment boundary-value problems to the analysis of periodic orbits in smooth and hybrid dynamical systems, quasi-periodic invariant tori, and homoclinic and heteroclinic connecting orbits between equilibria and/or periodic orbits;
• shows the use of vectorization for optimal computational efficiency, an object-oriented paradigm for the modular construction of continuation problems, and adaptive discretization algorithms for guaranteed bounds on estimated errors; and
contains extensive and fully worked examples that illustrate the application of the MATLAB®-based Computational Continuation Core (COCO) to problems from recent research literature that are relevant to dynamical system models from mechanics, electronics, biology, economics, and neuroscience.
This book is intended for students and teachers of nonlinear dynamics and engineering, as well as engineers and scientists engaged in modeling and simulation, and is valuable to potential developers of computational tools for analysis of nonlinear dynamical systems. It assumes some familiarity with MATLAB programming and a theoretical sophistication expected of upper-level undergraduate or first-year graduate students in applied mathematics and/or computational science and engineering.
About the Authors
Harry Dankowicz is Professor of Mechanical Science and Engineering at the University of Illinois at Urbana-Champaign. He is author of a research monograph on chaos in Hamiltonian systems and a textbook on multibody mechanics, and serves as an Associate Editor of the SIAM Journal on Applied Dynamical Systems.
Frank Schilder has held post-doctoral research and teaching positions at the University of Bristol, the University of Surrey, and the Technical University of Denmark. In addition to COCO, he is the author of TORCONT and RAUTO and co-author, with Claudia Wulff and Andreas Schebesch, of SYMPERCON.
Download the Continuation Core Toolbox
To request an examination copy or desk copy of this book, please use our online request form at www.siam.org/catalog/adopt.php.
Parameter continuation, manifold covering, toolbox development, boundary-value problems, computational bifurcation analysis
2013 / xvi + 584 / Softcover / 978-1-611972-56-6
List Price $99.00 / Member Price $69.30 / Order Code CS11