Continuation Core and Toolboxes (COCO) / Blog: Recent posts

A major new release of COCO was posted to the SourceForge site on January 28, 2025.

The following is a summary of changes since the previous release in August 2023 (more details below):

• New general-purpose support for analysis of continuation problems defined by constraints that are linearly dependent on the corresponding solution manifold, e.g., analysis of periodic orbits in problems with conserved quantities or bifurcation analysis for dynamical systems with symmetries.
• New general-purpose support for generic branch switching that is compatible also with analysis of symmetry-breaking bifurcations in dynamical systems with symmetries.
• New general-purpose support for detection, location, and handling of special points for piecewise-constant monitor functions associated with discrete jumps in their values.
• Associated updates to existing tutorial documentation and demos, and posting of a preprint on numerical bifurcation analysis for beginner and advanced users with particular interest in generic and non-generic bifurcation analysis of equilibria and periodic orbits.... read more

The paper Methods of continuation and their implementation in the COCO software platform with application to delay differential equations, published in Nonlinear Dynamics, Vol. 107, 3181- 3243 (2022), was recognized with the Best Paper Award for 2022 during the recent International Nonlinear Dynamics Conference, NODYCON 2023.

This paper reviews the role of continuation methods for bifurcation analysis and optimization, as well as the general construction paradigm of COCO and its compatibility with problems derived from variational principles. It further makes original contributions to a formulation of continuation problems describing suitably discretized delay-coupled multi-segment boundary-value problems with application to continuation of periodic orbits, quasiperiodic invariant tori, connecting orbits, and the solving of optimal control problems.

A major new release of COCO was posted to the SourceForge site on August 14, 2023. NOTE: a bug fix was posted on August 15, 2023

The following is a summary of changes since the previous release in March 2020 (more details below):

• New set of tutorial documentation and demos for beginner users with particular interest in basic bifurcation analysis of equilibria and periodic orbits.
• Updated handling of higher-order and directional derivatives of vector fields, including default implementations for finite-difference approximations, and upgrades to the COCO-compatible SYMCOCO toolbox for symbolic generation of COCO-compatible encodings of vector fields and their derivatives.
• Small change delivering a major punch with the addition of a 'norm' option to the atlas_1d algorithm in order to largely eliminate the sensitivity to mesh size that accompanies the default use of Euclidean norms.
• Significant upgrades to the handling of objects and persistent variables to ensure automatic garbage collection and plug memory leaks in the March 2020 release produced by the atlas_kd algorithm.... read more

A major new release of COCO was posted to the SourceForge site on March 22, 2020.

The following is a summary of changes since last announced release in November 2017 (more details below):

• Fully documented support (including tutorials and demos) for problem construction, including staged construction of adjoint equations, to allow for the application of the successive continuation paradigm to constrained design optimization problems with both equality and finite-dimensional inequality constraints, as documented in "Optimization with equality and inequality constraints using parameter continuation" by Li and Dankowicz.
• Fully documented support (including tutorials and demos) for parameter continuation along multi-dimensional solution manifolds in problems with adaptive discretization, as documented in "Multidimensional Manifold Continuation for Adaptive Boundary-Value Problems" by Dankowicz, Wang, Schilder, and Henderson.
• Support for symbolic generation of right-hand sides and their derivatives using the COCO-compatible SYMCOCO toolbox by Jan Sieber.... read more

A major new release of COCO was posted to the SourceForge site on November 17, 2017.

The following is a summary of changes since last announced release in November 2015 (more details below):

• Fully documented support for general-purpose, staged construction of adjoint equations, consistent with COCO’s object-oriented construction paradigm and the decomposition of continuation problems into coupled instances of individual continuation objects.
• Full support for adaptive remeshing of adjoint equations, consistent with adaptive updates to the problem discretization along families of solutions to integro-differential boundary-value problems.... read more

Since the November 1, 2015 release, two serious bugs have been corrected. Specifically,

• a bug in the implementation of the 'coll' toolbox for non-autonomous vector fields resulted in the use of an incorrect mesh of collocation nodes. Small, but significant differences were observed between bifurcation diagrams constructed using non-autonomous and autonomous implementations. This was corrected in the January 26, 2016 release.
• a bug in the implementation of the 'po' toolbox for continuation of saddle-node bifurcations in multi-segment periodic orbit problems resulted in an incorrect zero problem. This was corrected in the February 10, 2016 release.... read more

A major new release of COCO was posted to the SourceForge site on November 1, 2015.

The following is a summary of changes since last release in November 2014 (more details below):

• Fully documented, production-ready toolboxes with tutorials and demos for
  • Continuation and bifurcation analysis of equilibria in smooth dynamical systems;
  • Continuation of collections of constrained trajectory segments with independent adaptive discretization in autonomous or non-autonomous dynamical systems, including single- and multi-segment boundary-value problems.
  • Continuation and bifurcation analysis of single-segment periodic orbits in smooth, autonomous or non-autonomous dynamical systems, and multi-segment periodic orbits in hybrid, autonomous dynamical systems.... read more