The fuzziness appears when we need to perform, on manifold, calculations with imprecision variables.
A detailed description of slow invariant manifold calculations and canard detection and continuation is provided for the self-coupled FitzHugh Nagumo system within the AUTO manual, demo fnc.
In the case of the low-energy return method, methods using approximate manifold calculations for a Lissajous orbit and the direct transfer and injection to a libration-point orbit are proposed and shown to be useful.
The low-energy return method was investigated using the method of invariant manifold calculations for a Lissajous orbit, the method of direct libration-point orbit transfer and injection, and the control strategy used for a low-energy trajectory.
Note each system (dynamic or static inhibition) used to calculate a threshold manifold required the reduction x ˜ = x ˜ ∞ ( v ), for x = m, h, n, to allow calculation along repelling manifolds.
Note the system used here to calculate the threshold manifold makes use of the reduction x ˜ = x ˜ ∞ ( v ), for x = m, h, n, in order to allow calculation along the repelling middle branch.
The results of the CFD calculations demonstrate that the remodeled manifold without diffuser inlets and 6 mm diffuser front is the best among investigated designs with uniformity index of 0.996 and maximum standard flow deviation of 0.423%.
Overcoming the deficiencies of common small molecule force fields represents a particular challenge due to the considerable computational cost of high-level quantum-chemical calculations for predicting the conformational manifold.
By using the normal form theory and the center manifold theorem developed by Hassard [20] and the calculation methods in [21], we can determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions.
An experimental computer code is developed using a symbolic manipulator that performs the automated calculations necessary to calculate the varieties and to visualize the manifold.
