What is an invariant set in this context?

An invariant set is a subset of a dynamical system's phase space that is preserved by its flow, meaning any point starting in the set remains within it for all time steps.

Does this skill work with Julia programming?

Yes, it is designed to work with AlgebraicDynamics.jl, enabling the implementation of oapply for resource-sharing machines and compositional systems.

How does this skill use GF(3) triadic logic?

The skill participates in triadic composition where it is assigned a Trit of -1 (MINUS), representing sinks or absorbers, ensuring conservation across skill triplets in the system.

What is the Non-Backtracking Geodesic Qualification?

It is a condition that ensures skill invocation chains follow prime paths without revisiting states, using a Möbius filter to cancel out composite or backtracking paths.

Invariant Set Analysis

Name: Invariant Set Analysis
Author: plurigrid

byplurigrid

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Data Science & ML

Analyzes and identifies sets within dynamical systems that are preserved by the flow of differential equations and manifolds.

This skill provides a formal mathematical framework for analyzing invariant sets in dynamical systems, focusing on phase space regions that remain unchanged under a system's flow. It is particularly designed for identifying sinks and absorbers (Trit -1) and integrates deeply with AlgebraicDynamics.jl to facilitate compositional modeling of resource-sharing machines. By utilizing triadic composition (GF(3)) and Möbius filters, it ensures high-integrity modeling of complex system behaviors, making it essential for researchers and engineers working on stability, bifurcations, and long-term qualitative dynamics.

Key Features

01Integration with AlgebraicDynamics.jl for compositional modeling

022 GitHub stars

03Identification of sinks and absorbers in phase space

04Local and global qualitative behavior analysis of differential equations

05GF(3) triadic conservation for system state management

06Parameter-dependent bifurcation and stability assessment

Use Cases

01Designing compositional dynamical systems using Category Theory principles

02Modeling biological or chemical systems with stable end-states or absorbers

03Analyzing long-term stability and limit sets in physical manifolds

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi invariant-set

For use in Claude.ai and ChatGPT

Download Skill