in the phase portrait of a dynamical system, a heteroclinic orbit (sometimes called a heteroclinic connection) is a path in phase space which joins...

stable manifold and the unstable manifold of an equilibrium. It is a heteroclinic orbit–a path between any two equilibrium points–in which the endpoints are...

topological circle of equilibrium points and connecting heteroclinic orbits. If a heteroclinic cycle is asymptotically stable, approaching trajectories...

placed in a box, and the box is subjected to small horizontal oscillations, the pendulum may exhibit chaotic behavior. Homoclinic orbit Heteroclinic orbit...

the heteroclinic orbit. Equilibria connected by heteroclinic trajectories form heteroclinic cycles and cycles can be connected to form heteroclinic networks...

discretizing trajectories of a flow or iterating a map, periodic orbits and heteroclinic orbits can also be posed as a solution of F = 0 {\displaystyle F=0}...

usually accompanied by the birth or death of a periodic orbit. A transverse bifurcation of a heteroclinic cycle is caused when the real part of a transverse...

decreasing, but never actually reach the point. In other words, we have 4 heteroclinic orbits between the two saddle points. They intersect at two cycles around...

The weak conjecture says now, that the KPZ equation is the only Heteroclinic orbit between the KPZ and EW fixed point. If one fixes the time dimension...

fixed points together with homoclinic and heteroclinic orbits connecting these. Moreover, there is at most one orbit connecting different fixed points in the...