The book **Recipes for Continuation** introduces a large collection of tutorial toolboxes and examples explaining the philosophy of the computational continuation core (`COCO`

) that is implemented in the project **Continuation Core and Toolboxes**. It provides a comprehensive introduction into toolbox development within the development platform `COCO`

.

The book contains thousands of lines of explicit code examples. A fully documented version of this code is also available through the most recent **release**, as well as in the **SourceForge 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.

Please follow **this link** for instructions on how to install `COCO`

and the tutorial toolboxes and examples on your personal computer.

Follow **this link** for a series of video tutorials illustrating the installation and use of `COCO`

and `COCO`

toolboxes.

The primary source for the code associated with **Recipes for Continuation** is the book itself. In the **release**, the top-level **recipes** folder contains a contents file (named Contents.m) that can be explored using the Matlab documentation browser, by typing `doc`

followed by the name of the containing folder on the command line (assuming that the folder has been added to the search path through the execution of the `COCO`

-specific `startup.m`

file).

This contents file contains links to

- a list of toolbox development lines and demos ordered by chapter, which organizes the code by its appearance in the book.

- a list of figure demos ordered by figure number, which organizes the code by its use in generating individual figures in the book.

- a list of demos ordered by problem name, which organizes the code by specific problems considered inthe book.

The principles of continuation and the `COCO`

paradigm of problem construction are illustrated through a number of template toolboxes and atlas algorithms described in detail in **Recipes for Continuation**. These include:

**alg**,**compalg**: solutions to systems nonlinear equations, composite continuation problems**coll**,**varcoll**: orthogonal collocation for orbit segments of ODEs, variational collocation problem**bvp**,**msbvp**: single-segment- and mulit-segment boundary value problems**po**,**hspo**: periodic orbits of ODEs and hybrid systems**dft**: Fourier collocation method for periodic orbits**atlas1d**,**atlas2d**: computation of 1- and 2-dimensional solution manifolds

Several of these toolboxes and atlas algorithms are developed through multiple versions that illustrate successively higher levels of sophistication. In the repository, each version is contained in a separate folder and accompanied by a separate folder containing scripts and functions demonstrating its use and application to typical problems from the study of nonlinear dynamical systems.

The toolbox and atlas algorithm demos in **Recipes for Continuation** are applied to problems from several branches of applied mathematics and computational science. These include:

*bangbang*: Periodic orbits of the Duffing single-degree-of-freedom nonlinear oscillator under bang-bang excitation.*bratu*: Steady-state temperature distribution of an exothermic reaction in a 1-dimensional medium with boundaries connected to heat baths.*brusselator*: Equilibria of a 1-dimensional Brusselator model.*catenary*: Extremal curves of the catenary problem from the calculus of variation.*cusp*: Equilibria of the cusp normal form.*doedel*: Heteroclinic connections between known equilibria.*duffing*: Periodic orbits of the harmonically excited, Duffing single-degree-of-freedom mechanical oscillator.*henon*: Periodic orbits of the two-dimensional nonlinear Henon map.*huxley*: Heteroclinic connections between unknown equilibria.*impact*: Periodic orbits of a harmonically excited, single-degree-of-freedom, linear mechanical oscillator with impacts.*langford*: Quasiperiodic invariant tori and phase-locked, resonant periodic orbits.*lienard*: Periodic orbits of a planar Lienard dynamical system.*linode*: Transient and periodic orbits of a harmonically excited, single-degree-of-freedom, linear mechanical oscillator.*lorenz*: Heteroclinic connections between a known equilibrium and an unknown periodic orbit in the Lorenz system.*marsden*: Periodic orbits emanating from a Hopf bifurcation and homoclinic bifurcations.*pneta*: Periodic orbits of a slow-fast oscillator.*popul*: Equilibria in a model of population dynamics.*pwlin*: Periodic orbits of a piecewise smooth dynamical system.*stickslip*: Periodic orbits of a hybrid dynamical system modeling a harmonically excited, two-degree-of-freedom, nonlinear mechanical oscillator with impacts and friction.*tanh*: Interpolation of an equipartitioned sample of the function`tanh(p*t)/tahn(p)`

on a given interval.*tor*: Periodic orbits of a three-dimensional nonlinear dynamical system.*vanderpol*: Members of the canard family of periodic orbits of the forced Van-der-Pol equation.

Please follow **this link** to file a bug report for the code or supporting documentation associated with the book.