# replaceSymbolicParameters

Replaces symbolic parameter values of the model tensor by new (numeric or symbolic) values.

## Contents

- Syntax
- Description
- Example
- References
- See also

## Syntax

sys = sys.replaceSymbolicParameters(OLD, NEW) with OLD as the old symbolic parameter values as symbolic array, which will be replaced by new parameter values in NEW, either a symbolic or numeric array with the same length as OLD

Attention: For simulation it is mandatory that the parameters have numeric values.

## Description

The algorithm simply replaces symbolic paramter values with new parameter values which are stored in the continuous sparse matrices of sys.H, e.g. sys.H.F.state.c or sys.H.phi.equality.c

## Example

Sprott B Attractor

In [1] J. C. Sprott proposed chaotic attractor named Sprott A-S systems. The Sprott B attractor can be represented by the following model tensor

    H = hyCPN1();
    H.F.stateDerivative  = [1 0 0 0 0 0 0 0;...
                            0 1 0 0 0 0 0 0;...
                            0 0 1 0 0 0 0 0];
    H.F.state = [0 0 0 0 1 0 0 1;...
                 0 0 0 1 0 1 0 1;...
                 0 0 0 1 0 0 0 0];
    H.phi.equality =   [-1 0 0 sym("a") 0 0 0 0;...
                        0 -1 0 0 1 -sym("b") 0 0;...
                        0 0 -1 0 0 0 sym("c") -1];

A dmss model can be created from the tensor

    Ts = 0;
    sys = dmss(H,Ts);

Its equations can be visited by

    disp(sys.symbolicEquations)

      a*x2*x3 - xp1 == 0
    x1 - xp2 - b*x2 == 0
    c - xp3 - x1*x2 == 0

The symbolic parameters

    params = [sym("a"), sym("b"), sym("c")];

can be replaced by numeric values

    numParams = [0.4, 1.2, 1];

using

    sys = sys.replaceSymbolicParameters(params, numParams);
    disp(sys.symbolicEquations)

      (2*x2*x3)/5 - xp1 == 0
    x1 - (6*x2)/5 - xp2 == 0
        1 - x1*x2 - xp3 == 0

## References

[1] J. C. Sprott, “Some simple chaotic flows,” Physical Review E, vol. 50, no. 2, Aug. 1994. doi:10.1103/physreve.50.r647

## See also

dmss, dmsim, sym2dmss

Author(s): Torben Warnecke