Recipes for Continuation

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.
• 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.