What is the Lyapunov Stability skill for Claude?

It is a specialized skill that enables Claude to analyze the stability and qualitative behavior of differential equations and dynamical flows using advanced mathematical principles.

How does this skill interact with Julia?

It features a direct connection to AlgebraicDynamics.jl, allowing for the implementation of compositional dynamical systems and resource-sharing machine modeling.

What is the role of GF(3) logic in this skill?

The skill uses a triadic logic (Trit 0, +1, -1) where this specific skill acts as an Ergodic/Neutral element to maintain algebraic conservation across skill triplets.

Can this skill help with control theory?

Yes, it is specifically designed to evaluate the robustness of systems under perturbation, which is a fundamental requirement in control theory and engineering.

What does Non-Backtracking Geodesic Qualification mean?

It ensures that the skill's invocation chain follows a 'prime path' where states are not revisited, optimized via Möbius inversion filters for efficient analysis.

Lyapunov Stability Analysis

Name: Lyapunov Stability Analysis
Author: plurigrid

byplurigrid

0•

Ciencia de Datos y ML

Analyzes the stability of dynamical systems using Lyapunov's direct method and algebraic dynamics principles.

This skill provides specialized capabilities for understanding the qualitative behavior of differential equations and flows on manifolds. It enables Claude to perform rigorous stability analysis near equilibria and invariant sets, identify long-term global structures, and detect parameter-dependent bifurcations. Designed for researchers and engineers, it integrates with AlgebraicDynamics.jl for compositional modeling and utilizes a GF(3) triadic logic framework to ensure conserved transitions during complex system simulations.

Características Principales

01Evaluates global structure and long-term limit sets

02Integrates with AlgebraicDynamics.jl for resource-sharing machines

03Implements GF(3) conserved triadic composition logic

04Qualifies non-backtracking geodesic traversal via Möbius squarefree conditions

050 GitHub stars

06Analyzes local behavior near equilibria and invariant sets

Casos de Uso

01Verifying the robustness of control systems under perturbation

02Analyzing qualitative state changes and bifurcations in mathematical models

03Modeling compositional dynamical systems in Julia

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi lyapunov-stability

For use in Claude.ai and ChatGPT

Download Skill