What is semi-conjugacy in the context of this skill?

Semi-conjugacy is a surjective map between two dynamical systems that preserves the time-evolution of the systems, allowing one to understand a complex system through a simpler representation.

How does this skill integrate with Julia?

It provides specific patterns and implementation guidance for using AlgebraicDynamics.jl to model compositional dynamical systems and resource-sharing machines.

What are 'Trits' in this skill's context?

Trits refer to a GF(3) balanced ternary logic system where this skill acts as a 'PLUS' (Trit 1) generator within a triadic composition framework.

Can this skill be used for stability analysis?

Yes, it includes frameworks for evaluating the robustness of systems under perturbation and analyzing long-term dynamics like attractors and limit sets.

Dynamical Systems Semi-conjugacy

Name: Dynamical Systems Semi-conjugacy
Author: plurigrid

byplurigrid

•

Data Science & ML

Analyzes and maps the qualitative transformations between dynamical systems using topological semi-conjugacy methods.

This skill provides specialized mathematical tools for analyzing semi-conjugacy in dynamical systems theory, allowing Claude to define and evaluate surjective maps that intertwine distinct mathematical flows. It is designed for researchers and engineers working with differential equations, providing a framework to study equilibria, global structures, and bifurcations. By integrating with AlgebraicDynamics.jl, it facilitates compositional modeling of complex systems, ensuring that transformations between phase spaces maintain qualitative integrity and follow non-backtracking geodesic paths.

Key Features

01Equilibria and invariant set analysis for local behavior

028 GitHub stars

03Integration with AlgebraicDynamics.jl for compositional modeling

04Global structure evaluation for long-term dynamics and limit sets

05Surjective map intertwining for dynamical system comparison

06Bifurcation and stability analysis under parameter perturbations

Use Cases

01Analyzing the stability and robustness of resource-sharing machines in Julia

02Validating the qualitative behavior of differential equations using Möbius filter invariants

03Simplifying high-dimensional dynamical models into topologically equivalent lower-dimensional systems

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi semi-conjugacy

For use in Claude.ai and ChatGPT

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