equilibrium point
Let an agent explain equilibrium points and their classification, relay stability analysis and examples from dynamical systems and economics sources, describe hyperbolic and market equilibria, and distinguish equilibrium points from equilibrium in thermodynamics and chemistry and from steady states of open systems.
Research draft, second pass
A second pass drafted this model: the structure a model of this thing needs, and what is known about it in the world. The line under this one says how the second half was obtained - researched against sources, or recalled without web access, in which case nothing here was read anywhere and every claim is a lead to verify. Unreviewed either way.
Researched by: Claude
Bundle → Layer → Finding → Questions Filled
4 bundles · 8 layers · 8 findings · 16 questions
Understand What an equilibrium point is.
Definition
Definition.
Definition
Definition.
- What is an equilibrium point, and how does it differ from thermodynamic and chemical equilibrium and steady states? definition
- Is the question about mathematics, physics, ecology or economics? boundary
Types
Types.
Types
Types.
- What are stable, unstable, saddle and hyperbolic equilibrium points? definition
- Which entry fits the specific type? action
Analysis Stability analysis.
Linearisation
Linearisation.
Linearisation
Linearisation.
- How do eigenvalues and the Hartman-Grobman theorem classify equilibria? provenance
- Which references are standard? provenance
Lyapunov
Lyapunov methods.
Lyapunov
Lyapunov.
- How do Lyapunov functions establish stability without linearisation? provenance
- Which sources are cited? provenance
Applications Applications.
Economics
Market equilibrium.
Economics
Economics.
- What is market equilibrium, and how is it analysed for stability? provenance
- Which entry fits economic equilibrium? action
Science
Science and engineering.
Science
Science.
- How are equilibria used in mechanics, ecology, epidemiology and control? provenance
- Which entry fits control theory? action
Context Beyond points.
Bifurcation
Bifurcations.
Bifurcation
Bifurcation.
- How do equilibria appear, disappear and change stability in bifurcations? provenance
- Which entry fits bifurcation theory? action
History
History.
History
History.
- How did Poincare, Lyapunov and others develop equilibrium and stability theory? provenance
- Which entry fits the history of dynamical systems? action
Classifiers Filled
- Family
- Thing Registry
- Category
- Cross-cutting context
- Entry kind
- thing
- Plane
- XCT
- Domain
- XCT.STA
- Also called
- market equilibrium, Hyperbolic equilibrium point
What it is Filled
A state of a dynamical system in which the system remains at rest unless disturbed, a point where the rate of change is zero, classified as stable, unstable or saddle points and, when eigenvalues have no zero real part, as hyperbolic equilibrium points, with applications from mechanics and ecology to economics, where market equilibrium is the price and quantity at which supply equals demand; equilibrium points are the starting point for stability analysis.
Why it exists Filled
Let an agent explain equilibrium points and their classification, relay stability analysis and examples from dynamical systems and economics sources, describe hyperbolic and market equilibria, and distinguish equilibrium points from equilibrium in thermodynamics and chemistry and from steady states of open systems.
Distinguishing features Filled
- Zero rate of change
- Stability types
- Linearisation
- Cross-field use
What robots and AI may and may not do Derived, awaiting review
May
- explain the concept
- relay classification and analysis
- describe applications
- distinguish related concepts
Note: Affordances listed as what may be done; prohibitions collected from the text.
Moral aspects Missing, in the backlog
Not described yet. This gap is in the card backlog.
Owners Missing, in the backlog
Not described yet. This gap is in the card backlog.
Links to other meta-models Filled
parent
- Q11061286 - registry parent class
- Q3505845 - registry parent class
related
- equilibrium - in registry terms
- state - in registry terms
- stability theory - through linearisation
- market equilibrium - in economics
What else AI and robots need to interact with it Filled
Identity and identifiers required Filled
- Vercy registry: vr.tr.equilibrium-point
- Wikidata: Q1530271 (https://www.wikidata.org/wiki/Q1530271)
Direct properties not applicable Not applicable
- condition: derivative equals zero note
- hyperbolic: no eigenvalue with zero real part note
- Hartman-Grobman theorem: linearisation valid near hyperbolic points note
Plane XCT: no invented physical properties.
Recognition optional Filled
- State where the system s rate of change is zero
- Stable and unstable points, hyperbolic equilibrium point, market equilibrium
- Thermodynamic equilibrium is a macroscopic state; chemical equilibrium balances reactions; steady states may involve flows
- Not a visible object; a fixed point on a phase portrait.
Capabilities and actions required Filled
- explain the concept
- relay classification and analysis
- describe applications
- distinguish related concepts
Hazards and failure modes required Filled
- Confusing equilibrium points with thermodynamic equilibrium
- Linearising non-hyperbolic points
- Registry aliases mixing mathematics and economics
Standards and interfaces required Filled
- No regulation
Context of use required Filled
- Analysing rest states and stability.
- stable equilibrium points such as nodes and foci
- unstable and saddle points
- hyperbolic and non-hyperbolic equilibria
- market equilibrium in economics
- Nash equilibrium in game theory
- equilibria in ecological and epidemic models
Sources Missing, in the backlog
Not described yet. This gap is in the card backlog.
Note: Written from model knowledge without web access; claims are unverified.
Open questions
- Should market equilibrium and hyperbolic equilibrium be separate primary entries?
- How should dynamical systems sources be linked?
- The registry entry has merged aliases from mathematics and economics; should they be split off?
- Which entry fits the specific type?
- Which entry fits economic equilibrium?
- Which entry fits control theory?
Machine files
Provenance
thing registry research (pass 2) · unreviewed
Built from: models/things/publications/thing-q1530271/spec.json