## Breach doc: Simulations

The first thing one wants to do with a dynamical system is computing its evolution over time given some values for its initial conditions and various parameters. In Breach, this is done using the ComputeTraj command. It takes three arguments:

• A system Sys, obviously corresponding to the dynamical system under study
• A Parameter set P, which is a structure assigning values to parameters of the system
• A time specification time, which indicates the time instants for which we want to compute the state of system.

### Computing the nominal trajectory

The system structure Sys contains nominal (or default) values for the system parameters. To compute a trajectory corresponding to these nominal parameters, we can obtain the corresponding nominal parameter set by using the CreateParamSet routine. The example below shows how to do it for the Lorentz example (in Examples/Lorentz folder):

%% Init system and parameter set (create the Sys structure)
CreateSystem;

%% Create nominal parameter set
P0 = CreateParamSet(Sys);

%% Compute nominal trajectories and output result for t in [0 10] with time step .01
time = 0:.01:10;
Pf = ComputeTraj(Sys, P0, [0 10);


To plot the result, one can use two different routines. SplotTraj plots the result in the phase space (in this case, in the space $$(x_0,x_1, x_2)$$.). The code

SplotTraj(Ptraj)


produces:

SplotVar plots each variable of the simulation against time. Below is the output of

SplotVar(Ptraj)