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The system specification dialog box is where you specify your dynamical system (ODE). You call it by the Select|Systems|New command in the Main window (then it is still empty), or by clicking the edit button in the system list dialog box.

 

NOTES:

 

Listbox

What it is used for

Name system is where you type a name for your system.

Coordinates

is where you list names of phase (state) variables.

Parameters is where you list names of parameters your system depends on.
Time is where you type in the name of time variable, which must be a simple name.
 

Other fields are:

Component

What it does

Derivatives

is where you specify how the derivatives of the right-hand sides will be calculated. The choices made here are shown in the Derivatives information field in the Main window where i-th letter reflects your choice made for the derivatives of order i (i=1,2,3,4,5):

numerically

approximate derivatives by appropriate finite differences. This method will always work (as far as you functions can be differentiated at all). This choice is indicated by the letter 'N' in the Derivatives information field.

symbolically

this option is only possible when the symbolic toolbox of Matlab is present in your version. It automatically computes exact values of derivatives symbolically. This may take quite a while for large systems, but this is only upon system definition, and provides considerable acceleration and increased precision when computing curves. This choice is indicated by the letter 'S' in the Derivatives information field.

from a file

this option is only present if Matlab's symbolic toolbox is not available. When selecting this option a dialog box appears where you must enter the name of the file that contains the exact values of the derivatives in a specific format.

from window

This option is only available for derivatives of first or second order. You enter the exact values of the derivates in the corresponding editor space.
Editor area is where you specify your dynamical system. This component consists of one or three parts depending whether you have selected 'from window' to specify derivatives or not.

RHS

The first part is where you type in statements wich computes the values of right-hand sides. For example:
phi=3^((T-6.3)/10)
psialphaM=(25-V)/10
psialphaN=(10-V)/10
alphaM=psialphaM/(exp(psialphaM)-1)
alphaN=0.1*psialphaN/(exp(psialphaN)-1)
alphaH=0.07*exp(-V/20)
betaM=4*exp(-V/18)
betaN=0.125*exp(-V/80)
betaH=1/(1+exp((30-V)/10))
GTOT=gNa*M^3*H*(V-VNa)+gK*N^4*(V-VK)+gl*(V-Vl)
V'=(I-GTOT)/C
M'=phi*((1-M)*alphaM-M*betaM)
N'=phi*((1-N)*alphaN-N*betaN)
H'=phi*((1-H)*alphaH-H*betaH)
Be aware of the fact that you first have to declare your variables. There is just one equation per line.

derivates(1st or 2nd order)

Enter the exact values of the derivatives. You have to fill out everything otherwise the jacobian matrix will not be formed correctly. There will be an 'index exceeds dimension' error while doing computations using this system.

enter the jacobianp(hessianp)

Enter the exact values of the derivatives with respect to the parameters. Again you have to fill out everything or an error will be produced while doing computations using this system.
 

There are the following buttons at the bottom of the dialog box:

Button

What it does

OK

closes the dialog box, stores all the changes you have made in archives, constructs Matlab source text for the system, and makes the system the current system.

Cancel closes the dialog box without changing the specification of your system. All modifications you have made are lost.