Dynamical systems

Heteroclinic orbit

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 . (Wikipedia).

Heteroclinic orbit
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Related pages

Heteroclinic bifurcation | Equilibrium point | Heteroclinic cycle | Mathematics | Phase portrait | Dynamical system | Finite set | Periodic point | Stable manifold | Markov partition | Symbolic dynamics | Homoclinic orbit