Heteroclinic orbit
![The phase portrait of the pendulum equation x'' + sin x = 0. The highlighted curve shows the heteroclinic orbit from (x, x') = (−π, 0) to (x, x') = (π, 0). This orbit corresponds with the (rigid) pendulum starting upright, making one revolution through its lowest position, and ending upright again.](/Images/godic/202501/18/Heteroclinic_orbit_in_pendulum_phaseportrait4407.png")
In mathematics, in the phase portrait of a dynamical system, a heteroclinic orbit (sometimes called a heteroclinic connection) is a path in phase space which joins two different equilibrium points. If the equilibrium points at the start and end of the orbit are the same, the orbit is a homoclinic orbit.