saddle point

[′sad·əl ‚pȯint]

(geology)

(mathematics)

A point where all the first partial derivatives of a function vanish but which is not a local maximum or minimum.

For a matrix of real numbers, an element that is both the smallest element of its row and the largest element of its column, or vice versa.

For a two-person, zero-sum game, an element of the payoff matrix that is the smallest element of its row and the largest element of its column, so that the corresponding strategies are optimal for each player, given the strategy chosen by the other player.

The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Saddle Point

a critical point of a first-order differential equation. In a neighborhood of a saddle point, four half-line integral

Figure 1

curves enter the critical point. Between the four curves there are four regions, each of which contains a family of integral curves resembling hyperbolas (see Figure l). The pattern of integral curves in a neighborhood of a saddle point is reminiscent of the contour lines of a hyperbolic paraboloid, which has the shape of a saddle—hence the name of the critical point.

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References in periodicals archive

Here, there is notion of a critical saddle point of 2%.

Demographics lie in the eye of the beholder

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.

EXPERIMENTAL INVESTIGATION OF FLOW STRUCTURE DOWNSTREAM OF PERMEABLE CYLINDERS

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.

Effects of Informal Contracts on Innovative Cooperation among Enterprises in Industrial Clusters: An Evolutionary Game Analysis

According to the Karuch-Kuhn-Tucker conditions, a point of equilibrium for the A interaction is a saddle point for the win formula F [2], 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]?'.

Information transfer strategies or how to reach equilibrium and control in direct verbal communication

They cover linear optical response and Raman spectroscopy, nonlinear optical properties, terahertz response, saddle point spectroscopy, and device application.

Optical Properties of Graphene

In fact, such theorem considers a diffeomorphism [phi] possessing a transversal homoclinic point q to a hyperbolic saddle point p.

THE AMBROSETTI-PRODI PERIODIC PROBLEM: DIFFERENT ROUTES TO COMPLEX DYNAMICS

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.

An Efficient Numerical Contour Deformation Method for Calculating Electromagnetic Scattered Fields from 3-D Convex Scatterers

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.

Quantum Tunneling in Deformed Quantum Mechanics with Minimal Length

However, it is a saddle point under the following conditions:

An Analysis of the Replicator Dynamics for an Asymmetric Hawk-Dove Game

The saddle point method is used to determine the solution with zero group velocity.

Spatial-Temporal Instability of an Inviscid Shear Layer

For standard definitions of attracting fixed point, saddle point, stable manifold, and related notions see [10].

Bifurcation and Global Dynamics of a Leslie-Gower Type Competitive System of Rational Difference Equations with Quadratic Terms