# SIMbyom function derivatives.m (the model in ODEs)

Syntax: dX = derivatives(t,X,par,c)

This function calculates the derivatives for the model system. It is linked to the script file byom_sim_lorenz.m. As input, it gets:

*t*is the time point, provided by the ODE solver*X*is a vector with the previous value of the states*par*is the parameter structure*c*is the external concentration (or scenario number)

Time *t* and scenario name *c* are handed over as single numbers by call_deri.m (you do not have to use them in this function). Output *dX* (as vector) provides the differentials for each state at *t*.

- Author: Tjalling Jager (email: tjalling_at_debtox.info)
- Date: April 2015
- Web support: http://www.debtox.info/byom.php
- Back to index walkthrough_simbyom.html

## Contents

## Start

```
function dX = derivatives(t,X,par,c)
```

global glo % allow for global parameters in structure glo (handy for switches)

## Unpack states

The state variables enter this function in the vector *X*. Here, we give them a more handy name.

x = X(1); % state 1 y = X(2); % state 2 z = X(3); % state 3

## Unpack parameters

The parameters enter this function in the structure *par*. The names in the structure are the same as those defined in the byom script file. The 1 between parentheses is needed as each parameter has 5 associated values (probably not needed for the SIMbyom package).

sig = par.sig(1); % sigma rho = par.rho(1); % rho bet = par.bet(1); % beta

## Calculate the derivatives

This is the actual model, specified as a system of three ODEs:

```
dx = sig*(y-x);
dy = x*(rho-z)-y;
dz = x*y-bet*z;
dX = [dx;dy;dz]; % collect all derivatives in one vector dX
```