https://sourceforge.net/p/cocotools/wiki/functionality/Recent changes to functionalityenTue, 27 Oct 2015 20:43:19 -0000https://sourceforge.net/p/cocotools/wiki/functionality/<div class="markdown_content"><pre>--- v12 +++ v13 @@ -4,6 +4,7 @@ 1. **Continuation of equilibrium points** (`ep`). The `ep` toolbox provides algorithms for continuation of equilibria of autonomous vector fields. The `ep` toolbox is fully embeddable. Usage is demonstrated in multiple demos and fully documented in a tutorial manual. The toolbox supports - detection of codimension-1 bifurcation points (saddle-node bifurcations, Hopf bifurcations, and neutral saddle points) + - detection of codimension-2 bifurcation points (Bogdanov-Takens bifurcation along branch of Hopf bifurcations) - branch switching at branch points - continuation of saddle-node and Hopf bifurcation curves </pre> </div>Harry DankowiczTue, 27 Oct 2015 20:43:19 -0000https://sourceforge.netb0910c1d7906036a6ff84b53a41d98f272299f8ahttps://sourceforge.net/p/cocotools/wiki/functionality/<div class="markdown_content"><pre>--- v11 +++ v12 @@ -4,7 +4,6 @@ 1. **Continuation of equilibrium points** (`ep`). The `ep` toolbox provides algorithms for continuation of equilibria of autonomous vector fields. The `ep` toolbox is fully embeddable. Usage is demonstrated in multiple demos and fully documented in a tutorial manual. The toolbox supports - detection of codimension-1 bifurcation points (saddle-node bifurcations, Hopf bifurcations, and neutral saddle points) - - detection of branch and fold points - branch switching at branch points - continuation of saddle-node and Hopf bifurcation curves @@ -12,12 +11,10 @@ - monitoring of solutions to the corresponding variational problems - continuation of solutions to the corresponding variational problems - monitoring of the corresponding trajectory segment discretization errors - - detection of branch and fold points - branch switching at branch points + **Continuation of periodic orbits** (`po`). The `po` toolbox provides algorithms for continuation of single-segment periodic orbits in smooth autonomous or non-autonomous dynamical systems and of multi-segment periodic orbits in hybrid autonomous dynamical systems. The `po` toolbox is fully embeddable. Usage is demonstrated in multiple demos and fully documented in a tutorial manual. The toolbox supports - detection of codimension-1 bifurcation points (saddle-node bifurcations, period-doubling bifurcations, torus bifurcations, and neutral saddle points) - - detection of branch and fold points - branch switching at branch points - branch switching at Hopf bifurcations of equilibria - branch switching at period-doubling bifurcations </pre> </div>Harry DankowiczTue, 27 Oct 2015 20:42:35 -0000https://sourceforge.neta849680cec31c9deef1e0a0a6db2cb4d726818f0https://sourceforge.net/p/cocotools/wiki/functionality/<div class="markdown_content"><pre>--- v10 +++ v11 @@ -2,24 +2,20 @@ A new release of `COCO` is planned for November, 2015. This will include toolboxes for the following problems: -1. **Continuation of equilibrium points** (`ep`). The `ep` toolbox provides algorithms for continuation of equilibria of autonomous vector fields. The toolbox supports +1. **Continuation of equilibrium points** (`ep`). The `ep` toolbox provides algorithms for continuation of equilibria of autonomous vector fields. The `ep` toolbox is fully embeddable. Usage is demonstrated in multiple demos and fully documented in a tutorial manual. The toolbox supports - detection of codimension-1 bifurcation points (saddle-node bifurcations, Hopf bifurcations, and neutral saddle points) - detection of branch and fold points - branch switching at branch points - continuation of saddle-node and Hopf bifurcation curves -The `ep` toolbox is fully embeddable. Usage is demonstrated in multiple demos and fully documented in a tutorial manual. - -2. **Continuation of trajectory segments** (`coll`). The `coll` toolbox provides algorithms for continuation of constrained collections of trajectory segments for autonomous and non-autonomous vector fields, including multisegment boundary value problems. The toolbox relies on segment-specific adaptive discretizations using piecewise-polynomial interpolants and orthogonal collocation. The toolbox supports ++ **Continuation of trajectory segments** (`coll`). The `coll` toolbox provides algorithms for continuation of constrained collections of trajectory segments for autonomous and non-autonomous vector fields, including multisegment boundary value problems. The toolbox relies on segment-specific adaptive discretizations using piecewise-polynomial interpolants and orthogonal collocation. The `coll` toolbox is fully embeddable. Usage is demonstrated in multiple demos and fully documented in a tutorial manual. The toolbox supports - monitoring of solutions to the corresponding variational problems - continuation of solutions to the corresponding variational problems - monitoring of the corresponding trajectory segment discretization errors - detection of branch and fold points - branch switching at branch points -The `coll` toolbox is fully embeddable. Usage is demonstrated in multiple demos and fully documented in a tutorial manual. - -3. **Continuation of periodic orbits** (`po`). The `po` toolbox provides algorithms for continuation of single-segment periodic orbits in smooth autonomous or non-autonomous dynamical systems and of multi-segment periodic orbits in hybrid autonomous dynamical systems. The toolbox supports ++ **Continuation of periodic orbits** (`po`). The `po` toolbox provides algorithms for continuation of single-segment periodic orbits in smooth autonomous or non-autonomous dynamical systems and of multi-segment periodic orbits in hybrid autonomous dynamical systems. The `po` toolbox is fully embeddable. Usage is demonstrated in multiple demos and fully documented in a tutorial manual. The toolbox supports - detection of codimension-1 bifurcation points (saddle-node bifurcations, period-doubling bifurcations, torus bifurcations, and neutral saddle points) - detection of branch and fold points - branch switching at branch points @@ -27,9 +23,6 @@ - branch switching at period-doubling bifurcations - continuation of saddle-node, period-doubling, and torus bifurcation curves -The `po` toolbox is fully embeddable. Usage is demonstrated in multiple demos and fully documented in a tutorial manual. - - Available toolbox previews: 1. **Continuation in experiments** (CONTINEX). This toolbox implements a continuation method for noise contaminated zero problems. Examples are control based continuation in experiments and continuation for equation-free problems. The development of this toolbox was supported by the Danish research council (FTP) under the project number 0602-00753B. </pre> </div>Harry DankowiczTue, 27 Oct 2015 20:41:43 -0000https://sourceforge.net99dffb3e06c2015181a6cff061f5014878fe1c71https://sourceforge.net/p/cocotools/wiki/functionality/<div class="markdown_content"><pre>--- v9 +++ v10 @@ -10,7 +10,7 @@ The `ep` toolbox is fully embeddable. Usage is demonstrated in multiple demos and fully documented in a tutorial manual. -+ **Continuation of trajectory segments** (`coll`). The `coll` toolbox provides algorithms for continuation of constrained collections of trajectory segments for autonomous and non-autonomous vector fields, including multisegment boundary value problems. The toolbox relies on segment-specific adaptive discretizations using piecewise-polynomial interpolants and orthogonal collocation. The toolbox supports +2. **Continuation of trajectory segments** (`coll`). The `coll` toolbox provides algorithms for continuation of constrained collections of trajectory segments for autonomous and non-autonomous vector fields, including multisegment boundary value problems. The toolbox relies on segment-specific adaptive discretizations using piecewise-polynomial interpolants and orthogonal collocation. The toolbox supports - monitoring of solutions to the corresponding variational problems - continuation of solutions to the corresponding variational problems - monitoring of the corresponding trajectory segment discretization errors @@ -19,7 +19,7 @@ The `coll` toolbox is fully embeddable. Usage is demonstrated in multiple demos and fully documented in a tutorial manual. -+ **Continuation of periodic orbits** (`po`). The `po` toolbox provides algorithms for continuation of single-segment periodic orbits in smooth autonomous or non-autonomous dynamical systems and of multi-segment periodic orbits in hybrid autonomous dynamical systems. The toolbox supports +3. **Continuation of periodic orbits** (`po`). The `po` toolbox provides algorithms for continuation of single-segment periodic orbits in smooth autonomous or non-autonomous dynamical systems and of multi-segment periodic orbits in hybrid autonomous dynamical systems. The toolbox supports - detection of codimension-1 bifurcation points (saddle-node bifurcations, period-doubling bifurcations, torus bifurcations, and neutral saddle points) - detection of branch and fold points - branch switching at branch points </pre> </div>Harry DankowiczTue, 27 Oct 2015 20:41:02 -0000https://sourceforge.net1d1d554b60751a422b29be93e0ef4e1f39fb5148https://sourceforge.net/p/cocotools/wiki/functionality/<div class="markdown_content"><pre>--- v8 +++ v9 @@ -7,6 +7,7 @@ - detection of branch and fold points - branch switching at branch points - continuation of saddle-node and Hopf bifurcation curves + The `ep` toolbox is fully embeddable. Usage is demonstrated in multiple demos and fully documented in a tutorial manual. + **Continuation of trajectory segments** (`coll`). The `coll` toolbox provides algorithms for continuation of constrained collections of trajectory segments for autonomous and non-autonomous vector fields, including multisegment boundary value problems. The toolbox relies on segment-specific adaptive discretizations using piecewise-polynomial interpolants and orthogonal collocation. The toolbox supports @@ -15,6 +16,7 @@ - monitoring of the corresponding trajectory segment discretization errors - detection of branch and fold points - branch switching at branch points + The `coll` toolbox is fully embeddable. Usage is demonstrated in multiple demos and fully documented in a tutorial manual. + **Continuation of periodic orbits** (`po`). The `po` toolbox provides algorithms for continuation of single-segment periodic orbits in smooth autonomous or non-autonomous dynamical systems and of multi-segment periodic orbits in hybrid autonomous dynamical systems. The toolbox supports @@ -24,6 +26,7 @@ - branch switching at Hopf bifurcations of equilibria - branch switching at period-doubling bifurcations - continuation of saddle-node, period-doubling, and torus bifurcation curves + The `po` toolbox is fully embeddable. Usage is demonstrated in multiple demos and fully documented in a tutorial manual. </pre> </div>Harry DankowiczTue, 27 Oct 2015 20:40:44 -0000https://sourceforge.net3b9870ab98399f66a3c4b6a343b66940764ed474https://sourceforge.net/p/cocotools/wiki/functionality/<div class="markdown_content"><pre>--- v7 +++ v8 @@ -7,7 +7,7 @@ - detection of branch and fold points - branch switching at branch points - continuation of saddle-node and Hopf bifurcation curves - The `ep` toolbox is fully embeddable. Usage is demonstrated in multiple demos and fully documented in a tutorial manual. +The `ep` toolbox is fully embeddable. Usage is demonstrated in multiple demos and fully documented in a tutorial manual. + **Continuation of trajectory segments** (`coll`). The `coll` toolbox provides algorithms for continuation of constrained collections of trajectory segments for autonomous and non-autonomous vector fields, including multisegment boundary value problems. The toolbox relies on segment-specific adaptive discretizations using piecewise-polynomial interpolants and orthogonal collocation. The toolbox supports - monitoring of solutions to the corresponding variational problems @@ -15,7 +15,7 @@ - monitoring of the corresponding trajectory segment discretization errors - detection of branch and fold points - branch switching at branch points - The `coll` toolbox is fully embeddable. Usage is demonstrated in multiple demos and fully documented in a tutorial manual. +The `coll` toolbox is fully embeddable. Usage is demonstrated in multiple demos and fully documented in a tutorial manual. + **Continuation of periodic orbits** (`po`). The `po` toolbox provides algorithms for continuation of single-segment periodic orbits in smooth autonomous or non-autonomous dynamical systems and of multi-segment periodic orbits in hybrid autonomous dynamical systems. The toolbox supports - detection of codimension-1 bifurcation points (saddle-node bifurcations, period-doubling bifurcations, torus bifurcations, and neutral saddle points) @@ -24,7 +24,7 @@ - branch switching at Hopf bifurcations of equilibria - branch switching at period-doubling bifurcations - continuation of saddle-node, period-doubling, and torus bifurcation curves - The `po` toolbox is fully embeddable. Usage is demonstrated in multiple demos and fully documented in a tutorial manual. +The `po` toolbox is fully embeddable. Usage is demonstrated in multiple demos and fully documented in a tutorial manual. Available toolbox previews: </pre> </div>Harry DankowiczTue, 27 Oct 2015 20:40:25 -0000https://sourceforge.netd3f840dc8a649541404982d34479270a48146c89https://sourceforge.net/p/cocotools/wiki/functionality/<div class="markdown_content"><pre>--- v6 +++ v7 @@ -3,34 +3,28 @@ A new release of `COCO` is planned for November, 2015. This will include toolboxes for the following problems: 1. **Continuation of equilibrium points** (`ep`). The `ep` toolbox provides algorithms for continuation of equilibria of autonomous vector fields. The toolbox supports - - detection of codimension-1 bifurcation points (saddle-node bifurcations, Hopf bifurcations, and neutral saddle points) - detection of branch and fold points - branch switching at branch points - continuation of saddle-node and Hopf bifurcation curves - -The `ep` toolbox is fully embeddable. Usage is demonstrated in multiple demos and fully documented in a tutorial manual. + The `ep` toolbox is fully embeddable. Usage is demonstrated in multiple demos and fully documented in a tutorial manual. + **Continuation of trajectory segments** (`coll`). The `coll` toolbox provides algorithms for continuation of constrained collections of trajectory segments for autonomous and non-autonomous vector fields, including multisegment boundary value problems. The toolbox relies on segment-specific adaptive discretizations using piecewise-polynomial interpolants and orthogonal collocation. The toolbox supports - - monitoring of solutions to the corresponding variational problems - continuation of solutions to the corresponding variational problems - monitoring of the corresponding trajectory segment discretization errors - detection of branch and fold points - branch switching at branch points - -The `coll` toolbox is fully embeddable. Usage is demonstrated in multiple demos and fully documented in a tutorial manual. + The `coll` toolbox is fully embeddable. Usage is demonstrated in multiple demos and fully documented in a tutorial manual. + **Continuation of periodic orbits** (`po`). The `po` toolbox provides algorithms for continuation of single-segment periodic orbits in smooth autonomous or non-autonomous dynamical systems and of multi-segment periodic orbits in hybrid autonomous dynamical systems. The toolbox supports - - detection of codimension-1 bifurcation points (saddle-node bifurcations, period-doubling bifurcations, torus bifurcations, and neutral saddle points) - detection of branch and fold points - branch switching at branch points - branch switching at Hopf bifurcations of equilibria - branch switching at period-doubling bifurcations - continuation of saddle-node, period-doubling, and torus bifurcation curves - -The `po` toolbox is fully embeddable. Usage is demonstrated in multiple demos and fully documented in a tutorial manual. + The `po` toolbox is fully embeddable. Usage is demonstrated in multiple demos and fully documented in a tutorial manual. Available toolbox previews: </pre> </div>Harry DankowiczTue, 27 Oct 2015 20:39:46 -0000https://sourceforge.net2baab5e82864a8390263ecb56020c8ba3b2805ffhttps://sourceforge.net/p/cocotools/wiki/functionality/<div class="markdown_content"><pre>--- v5 +++ v6 @@ -9,7 +9,7 @@ - branch switching at branch points - continuation of saddle-node and Hopf bifurcation curves -The `ep`toolbox is fully embeddable. Usage is demonstrated in multiple demos and fully documented in a tutorial manual. +The `ep` toolbox is fully embeddable. Usage is demonstrated in multiple demos and fully documented in a tutorial manual. + **Continuation of trajectory segments** (`coll`). The `coll` toolbox provides algorithms for continuation of constrained collections of trajectory segments for autonomous and non-autonomous vector fields, including multisegment boundary value problems. The toolbox relies on segment-specific adaptive discretizations using piecewise-polynomial interpolants and orthogonal collocation. The toolbox supports @@ -19,7 +19,7 @@ - detection of branch and fold points - branch switching at branch points -The `coll`toolbox is fully embeddable. Usage is demonstrated in multiple demos and fully documented in a tutorial manual. +The `coll` toolbox is fully embeddable. Usage is demonstrated in multiple demos and fully documented in a tutorial manual. + **Continuation of periodic orbits** (`po`). The `po` toolbox provides algorithms for continuation of single-segment periodic orbits in smooth autonomous or non-autonomous dynamical systems and of multi-segment periodic orbits in hybrid autonomous dynamical systems. The toolbox supports @@ -30,7 +30,7 @@ - branch switching at period-doubling bifurcations - continuation of saddle-node, period-doubling, and torus bifurcation curves -The `po`toolbox is fully embeddable. Usage is demonstrated in multiple demos and fully documented in a tutorial manual. +The `po` toolbox is fully embeddable. Usage is demonstrated in multiple demos and fully documented in a tutorial manual. Available toolbox previews: </pre> </div>Harry DankowiczTue, 27 Oct 2015 20:38:56 -0000https://sourceforge.net2a3d8d5d19fd0169252866d97d075f12cb050ec1https://sourceforge.net/p/cocotools/wiki/functionality/<div class="markdown_content"><pre>--- v4 +++ v5 @@ -1,17 +1,38 @@ -The project _Continuation Core and Toolboxes_(`COCO`) is a development platform that provides a large amount of standard functionality required for investigating bifurcation problems and implementing toolboxes for new types of problems. The core was recently finished and the book [Recipes for Continuation]([wiki:recipes]) describes the underlying mathematics, the interface and toolbox development in great detail. +The project _Continuation Core and Toolboxes_ (`COCO`) is a development platform that provides a large amount of standard functionality required for investigating bifurcation problems and implementing toolboxes for new types of problems. The core was recently finished and the book [Recipes for Continuation]([wiki:recipes]) describes the underlying mathematics, the interface and toolbox development in great detail. -Toolboxes for standard problems will become available step by step. The current version of coco provides toolboxes for the following problems: +A new release of `COCO` is planned for November, 2015. This will include toolboxes for the following problems: -1. **Continuation of equilibrium points** (EP). The EP toolbox is a fully functional toolbox and provides algorithms for - - detection of co-dimension 1 bifurcation points (saddle-node-, Hopf- and neutral saddle points) - - detection of branch points - - branch switching at branch-points - - continuation of saddle-node- and Hopf bifurcation curves +1. **Continuation of equilibrium points** (`ep`). The `ep` toolbox provides algorithms for continuation of equilibria of autonomous vector fields. The toolbox supports -+ **Orthogonal collocation** (COLL). The COLL toolbox is an auxiliary toolbox that implements orthogonal collocation on a moving-mesh for orbit segments of ODEs. + - detection of codimension-1 bifurcation points (saddle-node bifurcations, Hopf bifurcations, and neutral saddle points) + - detection of branch and fold points + - branch switching at branch points + - continuation of saddle-node and Hopf bifurcation curves -+ **Continuation of periodic orbits** (PO). The PO toolbox implements a continuation problem for periodic orbits of ODEs. This toolbox is very basic right now and will be completed in the future. +The `ep`toolbox is fully embeddable. Usage is demonstrated in multiple demos and fully documented in a tutorial manual. -Toolboxes to be released soon (previews available under Toolbox Collection): ++ **Continuation of trajectory segments** (`coll`). The `coll` toolbox provides algorithms for continuation of constrained collections of trajectory segments for autonomous and non-autonomous vector fields, including multisegment boundary value problems. The toolbox relies on segment-specific adaptive discretizations using piecewise-polynomial interpolants and orthogonal collocation. The toolbox supports + + - monitoring of solutions to the corresponding variational problems + - continuation of solutions to the corresponding variational problems + - monitoring of the corresponding trajectory segment discretization errors + - detection of branch and fold points + - branch switching at branch points + +The `coll`toolbox is fully embeddable. Usage is demonstrated in multiple demos and fully documented in a tutorial manual. + ++ **Continuation of periodic orbits** (`po`). The `po` toolbox provides algorithms for continuation of single-segment periodic orbits in smooth autonomous or non-autonomous dynamical systems and of multi-segment periodic orbits in hybrid autonomous dynamical systems. The toolbox supports + + - detection of codimension-1 bifurcation points (saddle-node bifurcations, period-doubling bifurcations, torus bifurcations, and neutral saddle points) + - detection of branch and fold points + - branch switching at branch points + - branch switching at Hopf bifurcations of equilibria + - branch switching at period-doubling bifurcations + - continuation of saddle-node, period-doubling, and torus bifurcation curves + +The `po`toolbox is fully embeddable. Usage is demonstrated in multiple demos and fully documented in a tutorial manual. + + +Available toolbox previews: 1. **Continuation in experiments** (CONTINEX). This toolbox implements a continuation method for noise contaminated zero problems. Examples are control based continuation in experiments and continuation for equation-free problems. The development of this toolbox was supported by the Danish research council (FTP) under the project number 0602-00753B. </pre> </div>Harry DankowiczTue, 27 Oct 2015 20:38:27 -0000https://sourceforge.net284a6c67b1a0a028f2cb71107762dfc5fadbb557https://sourceforge.net/p/cocotools/wiki/functionality/<div class="markdown_content"><pre>--- v3 +++ v4 @@ -1,4 +1,4 @@ -The project *Continuation Core and Toolboxes* (coco) is a development platform that provides a large amount of standard functionality required for investigating bifurcation problems and implementing toolboxes for new types of problems. The core was recently finished and the book [Recipes for Continuation]([wiki:recipes]) describes the underlying mathematics, the interface and toolbox development in great detail. +The project _Continuation Core and Toolboxes_(`COCO`) is a development platform that provides a large amount of standard functionality required for investigating bifurcation problems and implementing toolboxes for new types of problems. The core was recently finished and the book [Recipes for Continuation]([wiki:recipes]) describes the underlying mathematics, the interface and toolbox development in great detail. Toolboxes for standard problems will become available step by step. The current version of coco provides toolboxes for the following problems: </pre> </div>Harry DankowiczTue, 27 Oct 2015 20:13:44 -0000https://sourceforge.net8d95395a848621c0286e87465abd58dd8121570b