Does this skill support Julia programming?

Yes, it specifically integrates with AlgebraicDynamics.jl to implement compositional dynamical systems and resource-sharing machines.

Can this skill help with stability analysis?

Yes, it provides tools for checking robustness under perturbation and evaluating the stability of specific paths or equilibrium points.

What is the primary purpose of the Trajectory skill?

It is designed to help analyze the qualitative behavior of solutions to differential equations and flows on manifolds within a defined phase space.

What does the 'Trit -1' designation mean?

Within its triadic composition framework, Trit -1 represents sinks or absorbers, helping to categorize the role of the trajectory in the system's global structure.

Trajectory Analysis

Name: Trajectory Analysis
Author: plurigrid

byplurigrid

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Ciencia de Datos y ML

Analyzes and models the paths of solutions through phase space within dynamical systems.

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The Trajectory skill provides specialized capabilities for Claude to analyze and interpret complex dynamical systems using phase space principles. It enables the qualitative assessment of differential equations, helping users identify local behaviors near equilibria and map global structures such as limit sets. By integrating with AlgebraicDynamics.jl and utilizing triadic composition (GF(3)), this skill allows for the rigorous modeling of resource-sharing machines, stability analysis, and the detection of bifurcations in mathematical or scientific computing workflows.

Características Principales

Integration with AlgebraicDynamics.jl for compositional systems
Global structure mapping for long-term dynamics and limit sets
Phase space path tracing and qualitative visualization
Bifurcation detection for parameter-dependent system changes
2 GitHub stars
Local behavior analysis for equilibria and invariant sets

Casos de Uso

Analyzing stability and sinks in multi-variable differential equations
Simulating resource-sharing machines via triadic composition and GF(3)
Modeling the evolutionary paths of complex chemical or biological systems

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Características Principales

Integration with AlgebraicDynamics.jl for compositional systems
Global structure mapping for long-term dynamics and limit sets
Phase space path tracing and qualitative visualization
Bifurcation detection for parameter-dependent system changes
2 GitHub stars
Local behavior analysis for equilibria and invariant sets

Casos de Uso

Analyzing stability and sinks in multi-variable differential equations
Simulating resource-sharing machines via triadic composition and GF(3)
Modeling the evolutionary paths of complex chemical or biological systems