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Heteroclinic orbit
Path between equilibrium points in a phase space / From Wikipedia, the free encyclopedia
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.
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Consider the continuous dynamical system described by the ordinary differential equation
Suppose there are equilibria at
Then a solution
is a heteroclinic orbit from
to
if both limits are satisfied:
This implies that the orbit is contained in the stable manifold of and the unstable manifold of
.