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

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数据科学与机器学习

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

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.

主要功能

01Mathematical validation via non-backtracking geodesic qualification

02Local equilibrium analysis using Jacobian matrix calculations

03Integration with AlgebraicDynamics.jl for compositional modeling

042 GitHub stars

05Bifurcation detection for parameter-dependent qualitative changes

06Stability classification including sinks, sources, and saddle points

使用场景

01Identifying critical bifurcation points in complex dynamical models

02Assessing the robustness of physical or chemical systems under perturbation

03Modeling and analyzing long-term dynamics and limit sets in differential equations

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi eigenvalue-stability

For use in Claude.ai and ChatGPT

Download Skill