Here, there is notion of a critical saddle point
For bare cylinder case, two focus points (F1, F2) emerge in the close region of cylinder and a saddle point
S occurs at the location which is considered at the end of vortex formation.
Stable Points DetJ TrJ Local Stability A(0, 0) + - ESS 5(0, 1) - Uncertainty Saddle point
C(1, 0) + + Unstable 0(1, 1) - Uncertainty Saddle point
Table 3: Local stability analysis of the evolution system.
According to the Karuch-Kuhn-Tucker conditions, a point of equilibrium for the A interaction is a saddle point
for the win formula F , The meaning of this result, namely of the term 'saddle point
' is revealed by the answer to the question: 'What does an optimum means of expression signify in the case of both initiators of interaction [DELTA]?'.
They cover linear optical response and Raman spectroscopy, nonlinear optical properties, terahertz response, saddle point
spectroscopy, and device application.
In fact, such theorem considers a diffeomorphism [phi] possessing a transversal homoclinic point q to a hyperbolic saddle point
The saddle point
[S.sub.*] corresponds to the point where the derivative of the phase function with respect to the t variable in the integrand in Equation (13) equals to zero.
Around a saddle point
[z.sub.0], where f'([z.sup.0]) = 0, there are two constant-phase (steepest) contours, on which Im f(z) is constant, passing through [z.sub.0] if f"([z.sub.0]) [not equal to] 0.
However, it is a saddle point
under the following conditions:
The saddle point
method is used to determine the solution with zero group velocity.
For standard definitions of attracting fixed point, saddle point
, stable manifold, and related notions see .