Dynamical Systems
Simulation Library in C++

Download the library for Linux (6k): Dynamical Systems Simulation in C++

Download the library for DOS/Borland C++ 3.1 including plotting functions (79k): Dynamical Systems Simulation in C++

Tip: In the DOS implementation, together with the numerical routines to calculate the temporal evolution of a Dynamical System, there is a set of classes designed to plot and to store the results.

• A Dynamical System is any part of the universe selected to study purposes that exibits a certain temporal evolution.
• Each Dynamical System has your own time, inputs, outputs and parameters.
• The Dynamical System can be linear or nonlinear.
• Its temporal behaviour is completely determined by the set of differential equations supplied in the Dynamical System definition.

One of the objectives in this project is to construct friendly implemented classes. The user must supply minimal information to getting started.
The main ContinuousDynamicalSystem class characteristics are:

• The class implemented for DOS, is a template, so it accepts many types of data. You can specify float, double, long double data types.
• The Linux implementation allows the user to set the precision by modifying the definition of the constant macro DSYSTEM_PRECISION in the header file "dsystem.h".
• The evolution of the system is computed via the fixed step Runge-Kutta fourth order algorithm.
• It is not necessary to informe the number of inputs, outputs, state variables and the number of parameters. These information are acquired in the construction of the derived class.
• All parameters in the Dynamical System are initialized to 1.
• You can utilize another class present in this module. The Vector class. With this class, you can simplify the interchange of information. See more details below.

In your header file (.H)

END_DECLARATION

where "Name" is the name of the derived class (the particular type of Dynamical System like Inverted_pendulum, Lorenz, etc).
If you want inputs in your system, you must write:

DECLARE_CONTINUOUS_DYNAMICAL_SYSTEM(Name)

DECLARE_INPUTS;

END_DECLARATION

If you want outputs:

DECLARE_CONTINUOUS_DYNAMICAL_SYSTEM(Name)

DECLARE_OUTPUTS;

END_DECLARATION

If you want inputs *and* outputs:

DECLARE_CONTINUOUS_DYNAMICAL_SYSTEM(Name)

DECLARE_INPUTS;
DECLARE_OUTPUTS;

END_DECLARATION

In your definition file (.CPP,.CC etc)

DEFINE_DIFFERENTIAL_EQUATION_SYSTEM(Name)

xdot[0] = p[0]*x[0] + x[1] + u[1];
xdot[1] = x[1] - p[1]*x[2]*u[0];
xdot[2] = x[0] - u[2];

END_DEFINITION

where:

xdot[n] - the nth state variable derivative.

x[n] - the nth state variable.

p[n] - the nth parameter.

u[n] - the nth input signal.

DEFINE_INPUTS

u[0] = 5.0;
u[1] = t;
u[2] = sin(t) - sqrt(x[0]);

END_DEFINITION

DEFINE_OUTPUTS

y[0] = x[0];
y[1] = (x[2] - x[1])/p[0];

END_DEFINITION

In the scope of MAIN or other function

Name system1,system2;        // Linux implementation.

Name<float> system1,system2; // For the DOS implementation.

Set the parameters and the time step of integration (for the Runge-Kutta fouth order algorithm).

system1.SetParameter(0, 1.34);
system1.SetParameter(1, 1.5);
system1.SetTimeStep(0.001);

system2.SetParameter(0, 2.4);
system2.SetParameter(1, 5.2);
system2.SetTimeStep(0.01);

Now, you can calculate the next states of the system(s):

system1.Evolve(); // go to the time t (current) + time_step.
system1.Evolve(tf); // go to the time tf through steps of time_step magnitude.
system1.Evolve(tf,dt); // go to the time tf through steps of dt.

Read the information that you need:

state = system1.GetStateVar(0);
out = system1.Output(1);
t = system1.GetTime();

Final Words
See the example for more details (files example.cpp and example.h).
Please, any sugestions send me an e-mail. I will really appreciate.

E-mail: torres@cpdee.ufmg.br

Download the library for Linux (6k): Dynamical Systems Simulation in C++

Download the library for DOS/Borland C++ 3.1 including plotting functions (79k): Dynamical Systems Simulation in C++