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.
Consider the continuous dynamical system described by the ODE
Suppose there are equilibria at and, then a solution is a heteroclinic orbit from to if
and
This implies that the orbit is contained in the stable manifold of and the unstable manifold of .
Read more about Heteroclinic Orbit: Symbolic Dynamics
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