How does it integrate with Julia?

It connects with the AlgebraicDynamics.jl library, treating linearization as a compositional dynamical system that implements oapply for resource-sharing machines.

What does 'Trit 0 (ERGODIC)' signify?

In the context of this skill's algebraic framework (GF(3)), Trit 0 represents a neutral or ergodic state that maintains conservation across skill triplets.

Does this skill support non-backtracking workflows?

Yes, it is qualified for non-backtracking geodesic traversal using Möbius inversion filters to ensure efficient state-path exploration without revisited states.

What is the primary purpose of the Linearization skill?

The skill is designed to approximate complex nonlinear behavior with simpler linear models, allowing for the analysis of local stability and qualitative dynamics near specific points.

Linearization Analysis

Name: Linearization Analysis
Author: plurigrid

byplurigrid

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データサイエンスとML

Approximates nonlinear dynamical systems using local linear models to analyze stability and phase space behavior.

概要

The Linearization skill empowers Claude to perform local approximations of complex, nonlinear differential equations and flows on manifolds within dynamical systems theory. It provides a robust framework for analyzing behavior near equilibria, understanding global structures, and identifying bifurcations in parameter-dependent models. Designed for scientific computing and advanced engineering, it integrates seamlessly with AlgebraicDynamics.jl and utilizes a unique triadic composition (GF(3)) to ensure algebraic consistency and non-backtracking geodesic qualification in automated reasoning tasks.

主な機能

Local approximation of nonlinear dynamics near equilibria
GF(3) triadic composition for ergodic and conserved state logic
Identification of bifurcations and parameter-dependent changes
Stability analysis and robustness testing under perturbation
Integration with AlgebraicDynamics.jl for compositional modeling
2 GitHub stars

ユースケース

Simplifying complex differential equations for control system design
Analyzing the stability of physical or biological systems near steady states
Investigating phase space behavior and limit sets in topological computing

概要

主な機能

Local approximation of nonlinear dynamics near equilibria
GF(3) triadic composition for ergodic and conserved state logic
Identification of bifurcations and parameter-dependent changes
Stability analysis and robustness testing under perturbation
Integration with AlgebraicDynamics.jl for compositional modeling
2 GitHub stars

ユースケース

Simplifying complex differential equations for control system design
Analyzing the stability of physical or biological systems near steady states
Investigating phase space behavior and limit sets in topological computing