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.

About

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

2 GitHub stars
Integration with AlgebraicDynamics.jl for compositional modeling
Analysis of equilibria and invariant sets in phase space
Modeling of parameter-dependent qualitative changes (bifurcations)
Stability assessment and robustness testing under perturbation
GF(3) conserved triadic composition for ergodic system balancing

Use Cases

Designing control systems for resource-sharing mechanical systems
Modeling ecological population dynamics where species exchange stability
Analyzing chemical reaction networks for phase transition points

About

Key Features

2 GitHub stars
Integration with AlgebraicDynamics.jl for compositional modeling
Analysis of equilibria and invariant sets in phase space
Modeling of parameter-dependent qualitative changes (bifurcations)
Stability assessment and robustness testing under perturbation
GF(3) conserved triadic composition for ergodic system balancing

Use Cases

Designing control systems for resource-sharing mechanical systems
Modeling ecological population dynamics where species exchange stability
Analyzing chemical reaction networks for phase transition points