Software MEP2 for analyzing the dynamical system with chamber structure

Victor Korobitsin, Julia Frolova

Version on November 24th, 2006 mep2.zip.

We present the software MEP2 realizing the numerical algorithms for analyzing the dynamical systems

dX/dt=F(t,X), X: R -> Omega (1)

with chamber structure Cs: union of closure of Ci, here Ci is a chamber of (1) that is Ci is an arcwise-connected subset of points where F is continuous.

The software MEP2 has the following features:

1. input the system with chamber structure in GUI Mode;
2. save and open the file with system;
3. graph the solution of system over time;
4. draw the projection of phase space on the plane and modify the trajectories of phase-plane portrait (add, delete and move the initial points);
5. visualize the phase space in three dimensions and change the viewport (rotate, move and scale).

The software allows to construct the elegant phase portrait of dynamical system and to view the specific character of solution trajectory in three dimension space. As distinct from other softwares the MEP2 may to calculate the solution for all chamber structures not for separate parts, i.e. indeed to solve the system with discontinues right-hand side.

The traditional algorithm permit to control for saving the precision of numerical solution inside continuous set Ci. But when the curve of solution crosses the boundary between chambers then this algorithm cannot gives the acceptable solution. Therefore we suggest the modernized algorithm for solving the (1). This algorithm corrects defect of classical numerical methods and permits to find the solution on boundary between chambers.

The software MEP2 is used for research in common project with group from The University of Kalmar, Sweden and for training the students of Computer Science Department, Omsk State University, Russia.

Coding parameters:

• language - C++
• compiler - Visual Studio C++ 6.0
• operating system - Windows 95 and higher

[1] Filippov, A. F., Differential Equations with Discontinuous Right-hand Sides. Mathematics and its Aplications (Soviet Series), Kluwer Academic, Boston, 1988.