What is the primary purpose of the Equilibrium skill?

It is designed to identify and analyze fixed points in dynamical systems, specifically where the vector field vanishes, to understand system stability and long-term behavior.

Can this skill be used for stability analysis?

Yes, it provides tools for analyzing both local behavior near equilibria and the global structure of invariant sets and bifurcations.

What is the relevance of the Möbius squarefree condition?

It serves as a qualifier for non-backtracking geodesic traversal, ensuring that the skill invocation chain follows unique paths without revisiting states.

How does it handle complex system compositions?

It utilizes GF(3) triadic logic and integrates with AlgebraicDynamics.jl, allowing for the composition of dynamical systems through resource-sharing machines.

What does the 'Trit 0' designation mean?

Trit 0 (ERGODIC) indicates a neutral or ergodic state within a triadic composition, ensuring the skill maintains conservation laws when used in triplets.

Equilibrium System Analyzer

Name: Equilibrium System Analyzer
Author: plurigrid

byplurigrid

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Ciencia de Datos y ML

Identifies and analyzes fixed points in dynamical systems where vector fields vanish to determine system stability.

The Equilibrium skill provides specialized capabilities for analyzing dynamical systems theory directly within Claude. It enables the identification of fixed points—states where the rate of change is zero—allowing users to explore qualitative behaviors of differential equations and flows on manifolds. By integrating with AlgebraicDynamics.jl and utilizing GF(3) triadic composition, it supports advanced modeling of resource-sharing machines and complex topological systems. It is particularly useful for researchers and engineers working with bifurcations, stability analysis, and global system structures where mathematical precision and non-backtracking geodesic qualification are required.

Características Principales

01Maintains GF(3) conservation across skill triplet compositions

02Analyzes local stability and global structure of dynamical flows

03Integrates with AlgebraicDynamics.jl for compositional system modeling

042 GitHub stars

05Identifies fixed points where vector fields vanish in phase space

06Detects bifurcations and parameter-dependent qualitative changes

Casos de Uso

01Developing compositional dynamical systems using resource-sharing architectures

02Analyzing long-term dynamics and limit sets in physical systems

03Modeling stability and fixed points in biological or chemical networks

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi equilibrium

For use in Claude.ai and ChatGPT

Download Skill