Heteroclinic orbit
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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 x = x0 and x = x1, then a solution φ(t) is a heteroclinic orbit from x0 to x1 if
and
This implies that the orbit is contained in the stable manifold of x1 and the unstable manifold of x0.
[edit] See also
[edit] References
- John Guckenheimer and Philip Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, (Applied Mathematical Sciences Vol. 42), Springer
