Fixed Point (Differential Equations)
Points of an Autonomous system of ordinary differential equations at which
If a variable is slightly displaced from a Fixed Point, it may (1) move back to the fixed point (``asymptoticallystable'' or ``superstable''), (2) move away (``unstable''), or (3) move in a neighborhood of the fixed point but not approach it(``stable'' but not ``asymptotically stable''). Fixed points are also called Critical Points orEquilibrium Points. If a variable starts at a point that is not a Critical Point, it cannotreach a critical point in a finite amount of time. Also, a trajectory passing through at least one point that is not aCritical Point cannot cross itself unless it is a Closed Curve, in which case it corresponds to a periodicsolution.
A fixed point can be classified into one of several classes using Linear Stability analysis and theresulting Stability Matrix.
See also Elliptic Fixed Point (Differential Equations), Hyperbolic Fixed Point (Differential Equations), Stable ImproperNode, Stable Node, Stable Spiral Point, Stable Star, Unstable Improper Node,Unstable Node, Unstable Spiral Point, Unstable Star- Baseball Cover
- Base Curve
- Base (Logarithm)
- Base (Neighborhood System)
- Base (Number)
- Base Space
- Basin of Attraction
- Basis
- Basis Theorem
- Basler Problem
- Basset Function
- Batch
- Bateman Function
- Batrachion
- Bauer's Identical Congruence
- Bauer's Theorem
- Bauspiel
- Bayes' Formula
- Bayesian Analysis
- Bayes' Theorem
- Bays' Shuffle
- Beam Detector
- Bean Curve
- Beast Number
- Beatty Sequence