Differential Equations Systems
Integrator and Researcher
Application package DESIR (Differential Equations Systems
Integrator & Research) for investigation of differential equations
systems. This package is devoted to the numerical investigation of ordinary
differential equations and maps on IBM compatible PC (MS-DOS) and is represented
by a collection of executed programs and libraries for
BORLAND TURBO PASCAL language (versions 5.5,6.0,7.0). The programs
being executed are designed to the introduction of new information to the
archive or to the choice of the existing system of differential equations,
to generating the program in TURBO PASCAL language for the given system
of equations,to starting of the TPC translator of the version corresponding
to the package libraries, and to starting of the created program of investigating
the system of differential equations.
The system under study should be given in the form: dY/dt=
F(t,Y,P) , where Y is the vector of N components (system's dimensionality,
maximum value of which equals 8) and P is the vector of parameters. Besides
the system itself, the matrix of linearized system (Jacobi matrix) should
The main features of the program are the following:
1. Construction of the trajectory of the given system
starting from the initial point in different projections in the graphic
windows of the screen.
2. Assignment of graphic windows (quantity, demensions,
coordinate axes) and of the regime of reflecting the trajectory on the
screen (color, step, visibility, etc.).
3. Assignment and change of the initial point and of any
parameter of the system.
4. Choice of the numeric method of solving the system
of differential equations (possible methods: Adams, Runge-Kutta, Gear,
extrapolation), of solving the eigenvalues and eigenvectors of matrix (Jacobi
or HQR methods) etc.
5. Search of equilibrium points (its eigenvalues, analysis
of criticals cases) of the given system, of periodic solutions (cycles
and its multiplicators), movement along one parameter with the search of
equilibrium points and cycle bifurcation, construction of Poincare-maps,
compu tation of the spectrum of Lyapunov and of fractal dimension,of the
number of rotation of quasi-periodic regimes, construction of 3-dimensional
6. Saving of the current state to the disk with further
continuation of the research starting from the saved spot.
7. Storing information about all systems studied previonsly
and their states.
DESIR package can be used in research connected with
ordinary differential equations (mathematical modeling in mechanics, physics,
chemistry, biology, ecology) and in teaching students courses of differential
equations, bifurcation theory, mathematical modeling, chaotic dynamics,