Fig. 3

Numerical simulation for \(N=200\) agents, \(\rho = 1\), \(\sigma = 0.07\) and \(M = 4\), until time \(T = 25 [s]\) (left) or \(T = 50 [s]\) (center and right). Left Hamiltonian function with three attracting poles \(H(X,Y) = ((X-1)^2 + Y^2) \cdot ((X+\frac{1}{2})^2 + (Y - \frac{\sqrt{3}}{2})^2) \cdot ((X+\frac{1}{2})^2 + (Y + \frac{\sqrt{3}}{2})^2)\). Center Asymmetric Hamiltonian function \(H(X,Y) = (((X-\frac{1}{2})^2 + Y^2) \cdot ((X+\frac{1}{2})^2 + (Y - \frac{\sqrt{3}}{2})^2) \cdot ((X+\frac{3}{4})^2 + (Y+\frac{\sqrt{27}}{4})^2))^{\frac{1}{3}}\). Right Hamiltonian function \(H(X,Y) = (((X-1)^2 + Y^2) \cdot ((X+1)^2 + Y^2) \cdot (X^2 + (Y-4)^2))^{\frac{1}{3}}\), resulting in two disconnected orbits