Is this skill suitable for non-linear systems?

Yes, it uses local linearization via the Jacobian to understand the behavior of non-linear systems near fixed points.

What types of stability can it identify?

It can identify local stability behaviors such as stable nodes, unstable sources, saddle points, and neutral stability near equilibria.

Can this skill be used with Julia programming?

Yes, it specifically includes patterns for integration with AlgebraicDynamics.jl to support compositional dynamical system modeling.

What is the primary function of the Eigenvalue Stability skill?

The skill provides a framework for classifying the stability of equilibrium points in dynamical systems by analyzing the eigenvalues of the Jacobian matrix.

What is the significance of the GF(3) integration mentioned?

It refers to a triadic composition framework where the skill acts as a 'Source' (Trit 1) to ensure algebraic conservation across a set of related mathematical skills.

Eigenvalue Stability Analysis

Name: Eigenvalue Stability Analysis
Author: plurigrid

byplurigrid

•

データサイエンスとML

Classifies the stability of dynamical systems by calculating and interpreting Jacobian eigenvalues for equilibrium analysis.

概要

The Eigenvalue Stability skill enables Claude to perform rigorous qualitative analysis of dynamical systems. It focuses on the classification of stability near equilibria and invariant sets by calculating Jacobian eigenvalues, allowing users to understand local behavior, identify global structures, and detect parameter-dependent bifurcations. Designed for engineers and mathematicians working with flows on manifolds, it integrates with AlgebraicDynamics.jl and utilizes GF(3) triadic composition and non-backtracking geodesic invariants to ensure robust and mathematically sound modeling of complex systems.

主な機能

Mathematical validation via non-backtracking geodesic qualification
Local equilibrium analysis using Jacobian matrix calculations
Integration with AlgebraicDynamics.jl for compositional modeling
2 GitHub stars
Bifurcation detection for parameter-dependent qualitative changes
Stability classification including sinks, sources, and saddle points

ユースケース

Identifying critical bifurcation points in complex dynamical models
Assessing the robustness of physical or chemical systems under perturbation
Modeling and analyzing long-term dynamics and limit sets in differential equations

概要

主な機能

Mathematical validation via non-backtracking geodesic qualification
Local equilibrium analysis using Jacobian matrix calculations
Integration with AlgebraicDynamics.jl for compositional modeling
2 GitHub stars
Bifurcation detection for parameter-dependent qualitative changes
Stability classification including sinks, sources, and saddle points

ユースケース

Identifying critical bifurcation points in complex dynamical models
Assessing the robustness of physical or chemical systems under perturbation
Modeling and analyzing long-term dynamics and limit sets in differential equations