Toolbox Library

Toolbox Library

Contents

At the heart of SSMTool there are three classes, namely

Each of these classes is responsible for a certain part of the analysis, as displayed in the figure below. Note that the manifold class can be used to compute general type invariant manifolds, such as LSMs as well. In the context of SSM-analysis, it is used as an engine to compute SSMs.

DynamicalSystem

To store a dynamical system the DynamicalSystem is used. Furthermore this class also provides routines for analysing the full dynamical system, and for investigating the (reduced) spectral properties of the linear part.

Methods

Manifold

To compute and store invariant manifolds. the Manifold class is used. A set of methods are used to solve the invariance equations and compute the manifolds.

Methods

Spectral Submanifolds

To compute Spectral Submanifolds the SSM class is used. It is a subclass of the Manifold class.

Methods

The following methods are provided for the analysis of the reduced dynamics. For directly computing forced response curves, backbone curves and stability diagrams, the following functions are provided

For the general continuation of the reduced dynamics:

ep toolbox:

po toolbox:

tor toolbox:

Other methods

Supplemental functionalities

Additional, custom built, functionalities for displaying and analysing the results of an SSM-computation are provided in the Features section.

Furthermore SSMTool is coupled with the continuation toolbox COCO. A wrapper for this toolbox is provided in

Wrappers