DSWeb Dynamical Systems Software aims to collect all available software on dynamical systems theory. This project was originally launched during the special year Emerging Applications of Dynamical Systems, 1997/1998, at the Institute for Mathematics and its Applications. The information here includes functionality, platforms, languages, references, and contacts.

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Construct center manifolds of ODEs or DDEs

Via this web page you obtain a center manifold of your specified system of ordinary differential equations (ODE) or delay differential equations (DDE), when the ODE/DDE has fast and center modes

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http://www.maths.adelaide.edu.au/anthony.roberts/gencm.php provides a web service to algebraically construct center manifolds of any ODE/DDE that you enter. The centre modes may be slow, as in a pitchfork bifuraction, or oscillatory, as in a Hopf bifurcation, or some more complicated superposition. In the case when the fast modes all decay, the centre manifold supplies you with a faithful large time model of the dynamics. For example, this web page could help you analyse the long time dynamics of the system \[ \frac{d\vec u}{dt}=\vec f(\vec u) =\left[\begin{array}{ccc} 2&1&2\\ 1&-1&1\\ -3&-1&-3 \end{array}\right] \vec u +\varepsilon \left[\begin{array}{c}u_2u_3\\ -u_1u_3\\ -u_1u_2\end{array}\right]. \] As this system is already entered for you, just enter the magic word, then click on the Submit button to see. Alternatively, you can obtain the equivalent modulation equations corresponding to a given set of ODE/DDEs that have one or more oscillatory modes (a Hopf bifurcation for example). The analysis provides you with equations for the evolution of the complex amplitudes of the oscillators. This approach is better than averaging/homogenisation.
KeywordsBifurcation analysis, Control, Identification
Model
  • ODEs
  • DDEs
Software Type
  • Other
Language
  • Other
Platform
  • Unix
  • Linux
  • Windows
  • MacOS
Availability
Contact Person
Tony Roberts, University of Adelaide
Categories: Software
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