Is this skill suitable for non-linear dynamics?

Yes, it is designed to analyze the qualitative changes in non-linear systems, including bifurcations and the robustness of limit sets under perturbation.

What is the primary function of the Dynamical System Functor skill?

It provides a mathematical framework to treat dynamical systems as functors, allowing for the composition and analysis of complex temporal behaviors and phase space transformations.

How does this skill integrate with Julia?

It specifically implements patterns compatible with AlgebraicDynamics.jl, facilitating the use of 'oapply' for resource-sharing machines and compositional modeling.

What does GF(3) conservation mean in this context?

The skill participates in a triadic composition system where the sum of trits (state values) must remain conserved (≡ 0 mod 3) across skill triplets to ensure system equilibrium.

Dynamical System Functor

Name: Dynamical System Functor
Author: plurigrid

byplurigrid

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데이터 과학 및 ML

Models and analyzes the categorical structure of dynamical systems to evaluate stability and qualitative behavior.

소개

The Dynamical System Functor skill provides a formal categorical framework for understanding the evolution of phase spaces over time. By leveraging dynamical systems theory and algebraic structures, this skill enables Claude to analyze local behavior near equilibria, predict global long-term dynamics, and evaluate parameter-dependent bifurcations. It is specifically designed for complex modeling tasks involving differential equations, resource-sharing machines, and topological computing, integrating seamlessly with tools like AlgebraicDynamics.jl and GF(3) triadic composition principles.

주요 기능

Categorical analysis of phase space and temporal flows
Non-backtracking geodesic traversal via Möbius squarefree filtering
Compositional dynamics using AlgebraicDynamics.jl patterns
2 GitHub stars
Stability and robustness evaluation under system perturbations
Local and global behavior modeling for invariant sets

사용 사례

Analyzing stability and limit sets in high-dimensional differential equations
Modeling complex resource-sharing machines and compositional systems
Designing topological computing paths using GF(3) conservation laws

소개

주요 기능

Categorical analysis of phase space and temporal flows
Non-backtracking geodesic traversal via Möbius squarefree filtering
Compositional dynamics using AlgebraicDynamics.jl patterns
2 GitHub stars
Stability and robustness evaluation under system perturbations
Local and global behavior modeling for invariant sets

사용 사례

Analyzing stability and limit sets in high-dimensional differential equations
Modeling complex resource-sharing machines and compositional systems
Designing topological computing paths using GF(3) conservation laws