What is the significance of the GF(3) Trit 0 designation?

The 'Trit 0' (ERGODIC) status signifies a neutral/ergodic state within a triadic composition, ensuring conservation laws are met across skill triplets.

What is a transcritical bifurcation in this context?

It is a type of local bifurcation where two fixed points (equilibria) collide and exchange their stability properties as a parameter is varied.

Does this skill support non-backtracking geodesic traversal?

Yes, it is qualified for non-backtracking traversal provided the Möbius squarefree condition is met, ensuring no states are revisited in the invocation chain.

How does this skill integrate with Julia?

The skill is built to connect with AlgebraicDynamics.jl, allowing users to implement transcritical transitions as compositional dynamical systems.

Transcritical Bifurcation Analysis

Name: Transcritical Bifurcation Analysis
Author: plurigrid

byplurigrid

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Data Science & ML

Analyzes and models dynamical systems where equilibria exchange stability through transcritical bifurcations.

Transcritical is a specialized Claude Code skill designed for researchers and engineers working within the domain of Dynamical Systems Theory. It provides a robust framework for investigating qualitative changes in differential equations, specifically focusing on the exchange of stability between equilibria. By integrating with AlgebraicDynamics.jl and utilizing GF(3) triadic composition, this skill enables precise mapping of phase space transitions, stability robustness under perturbations, and the analysis of long-term global structures for complex flows on manifolds.

Key Features

012 GitHub stars

02Integration with AlgebraicDynamics.jl for compositional modeling

03Analysis of equilibria and invariant sets in phase space

04Modeling of parameter-dependent qualitative changes (bifurcations)

05Stability assessment and robustness testing under perturbation

06GF(3) conserved triadic composition for ergodic system balancing

Use Cases

01Designing control systems for resource-sharing mechanical systems

02Modeling ecological population dynamics where species exchange stability

03Analyzing chemical reaction networks for phase transition points

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi transcritical

For use in Claude.ai and ChatGPT

Download Skill