Russian version

MATDS

Sorry, but this page and MATDS are under construction now!

MATDS is a MATLAB-based program for dynamical system investigation. It will be MATLAB-version of DESIR program. MATDS is a graphical MATLAB package for the interactive numerical study of dynamical systems. It works with version 6.5* of MATLAB. Now only ordinary differential equation study

Current version is 1.0 beta.

Author: Govorukhin V.N. E-Mail: vgov@math.rsu.ru, matds@nm.ru

Short description of current version


Installation and start MATDS

To install the package you need make a MATDS directory, copy matds.zip-file to this directory and run unzip -a matds.zip. This creates a subdirectories of MATDS with all necessary files. MATDS directory must be added to MATLAB path or must be a current work directory for MATLAB. For start MATDS type matds in matlab main window.

MATDS directory structure:

Example:

Fig.1. MATLAB windows with MATDS output

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Main menu and window

Information about current working status displays in main window.

Class - type of dynamical system.

System - name of system.

Fig.2. Main menu of MATDS

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Output of results

(see Fig. 1)

Fig.3. 2D output window.

Fig.4. 3D output window.

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Dynamical system definition

 

Fig.5. Menu of the first step of system definition

Fig.6. Window for system editing (second step of definition)

 

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Numerical integration of ODE system

In the program all standard methods of MATLAB ODE suite are included, and also additional means are used: integrators of high accuracy ode78 and ode87.

Examples:

Fig.7. Chaotic trajectory in Chua system

Fig.8. Trajectories in ABC-flow (ODE system with

periodic right hand side)

Some special integrators (simplectic, stiff etc.) will be added in next versions!

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Vector field visualization

 

Examples:

Fig.9. Tube plot corresponding to Lorenz attractor.

Fig.10. Vector field and limit cycle

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Equilibria analysis

Now only finding of equilibria and stability analysis for fixed value of parameter is possible in MATDS. Newton method used for equilibria finding. Current initial point (main menu -> Edit -> Initial point) is a initial condition for Newton method. Stable equilibria is depicted by green circle and ustable ones by red.

Examples:

Fig.11. Three unstable equilibria in Lorenz system.

Continuation equilibria along parameters with elements of bifurcation analysis will be added in next versions!

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Periodic solutions

Will be added in next versions...

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Poincare map

Now exist two types of Poincare map in MATDS: Section by time (output points of trajectory with fixed time interval); Section by plane in phase space. Type of map and equation of plane or time interval can be defined in dialog window. For activate Poincare map calculation user must

Fig.12. Poincare map by time definition

Fig.13. Poincare map by plane definition

 

Fig.14. Two Poincare section and chaotic trajectory for ABC flow.

Fig.15. Poincare map for Ueda attractor (by time).

 

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Lyapunov exponents

To activate Lyapunov exponents calculation user must call Research->Lyapunov item in main MATDS menu. After that Number of exponents k (0<k<=dimension of syste), step of averaging for algorithm (see, A. Wolf, J. B. Swift, H. L. Swinney, and J. A. Vastano, "Determining Lyapunov Exponents from a Time Series," Physica D,
 Vol. 16, pp. 285-317, 1985.) and step of values output must be defined.

Fig.16. Options menu for Lyapunov exponents calculation. 

Fig. 17. Lyapunov exponents for Lorenz system (value of parameters: R=28, b=8/3, sigma=10).

Will be added in next versions...

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Download and installation MATDS

Now MATDS is under construction and can be a bugs, sorry...

The author will be very grateful to any information on work of the program both any remarks and suggestions!

To download what you need, simply click on the appropriate links below. The file matds.zip contains the latest version of the package.

Download last version of MATDS

If you want to receive the information on MATDS and development of the program send E-Mail to author with subject MATDS.

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Last modification 20 May 2004

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