# 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.

## 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