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.
function dX = derivatives(t,X,par,c)
global glo % allow for global parameters in structure glo (handy for switches)
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
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