Stability of equilibria

The above equilibria and periodic orbits (with exception of the laminar state) are never seen in simulations and experiments because they are unstable. Fortunately, they are not very unstable. And in fact, we do observe close passes to the least unstable equilibria in simulations.

Within the S-invariant subspace the number of unstable eigendirections is small, and the leading eigenvalues are nicely separated into a few positive, exponentially expanding and (infinity of) negative, exponentially contracting ones:

 

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As these stabilities have to be computed in 60K-dimensional statespaces, their evaluation was one of the most challenging computational problems encountered here.

• LM: laminar equilibrium
• LB, UB: Nagata lower and upper branch equilibria.
• NB, NB2, and EQ5: new equilibria.