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Recipes for Continuation

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by Harry Dankowicz and Frank Schilder


2013 / xvi + 584 / Softcover / ISBN 978-1-611972-56-6 / List Price $99.00 / Member Price $69.30 / Order Code CS11

Keywords: parameter continuation, manifold covering, toolbox development, boundary-value problems, computational bifurcation analysis

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Recipes for Continuation 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. The presentation

  • 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.

Recipes for Continuation provides a comprehensive introduction into toolbox and atlas algorihtm development within the development platform COCO. The book contains thousands of lines of explicit code examples. A fully documented version of this code is available for download from an online repository. This includes source code for all toolboxes and atlas algorithms, demo scripts that reproduce example input and output, and figure-generating functions that recreate essential aspects of the corresponding figures in the book. High-resolution .pdf versions of the figures from the book are also available for download.

Follow this link for a series of video tutorials illustrating the installation and use of COCO and COCO toolboxes.

Recipes for Continuation 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.

ISBN 9781611972566 


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