Figure 3

Space mapping trajectories for 1–6 dogs. The simulations are stopped if \(| \bar{X} - Z_{\mathrm{des}}| < 0.05\) holds true. The corresponding times are \(T_{1} =3400, T_{2} = 80, T_{3} = 60, T_{4} = 60, T_{5} = 70, T_{6} = 40\), where the subscript refers to the number of dogs involved in the simulation. We see that already one dog is able to steer the crowd. Nevertheless, more dogs significantly decrease the time needed for the steering process. The stochastic influence in the system is implicitly displayed in the trajectory of the dogs in the figure on the top left. As for deterministic systems one would expect to have a homogeneous helix