How does it handle nullclines and equilibrium points?

The skill provides patterns for identifying and plotting nullclines, which are the lines where the derivative of one variable is zero, helping to locate equilibria.

Does this skill require specific Python libraries?

Yes, the generated code typically utilizes NumPy for numerical computation and Matplotlib for rendering the streamplots and vector fields.

What types of systems can I visualize with this skill?

It is optimized for 2D autonomous dynamical systems defined by ordinary differential equations (ODEs).

Can I use this for bifurcation analysis?

Absolutely; it is specifically designed to work in tandem with the bifurcation-generator skill to show how state space changes across parameters.

Is it suitable for non-linear oscillators?

Yes, it is ideal for visualizing non-linear systems such as the Van der Pol oscillator or Lotka-Volterra predator-prey models.

Phase Portrait Generator

Name: Phase Portrait Generator
Author: plurigrid

byplurigrid

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データサイエンスとML

Generates visual phase portraits and vector fields for 2D dynamical systems to analyze state space behavior.

概要

The Phase Portrait Generator skill empowers Claude to visualize complex 2D autonomous systems by generating comprehensive phase portraits. It automates the creation of vector fields, nullclines, and trajectories, providing essential insights into equilibria and system stability. Designed for researchers and engineers working with differential equations, it seamlessly integrates with bifurcation analysis workflows to map state space transitions and dynamical behavior in topological contexts, making it an essential tool for modeling and simulating non-linear systems.

主な機能

Plotting of nullclines and system equilibria points
Seamless integration with bifurcation detection skills
Trajectory analysis within 2D state space
2 GitHub stars
Automated vector field visualization for 2D autonomous systems
High-quality streamplot generation using Matplotlib

ユースケース

Documenting nonlinear dynamics through automated state space plotting
Visualizing the behavior of oscillators like the Van der Pol oscillator
Analyzing stability and equilibrium in chemical or biological dynamical models

概要

主な機能

Plotting of nullclines and system equilibria points
Seamless integration with bifurcation detection skills
Trajectory analysis within 2D state space
2 GitHub stars
Automated vector field visualization for 2D autonomous systems
High-quality streamplot generation using Matplotlib

ユースケース

Documenting nonlinear dynamics through automated state space plotting
Visualizing the behavior of oscillators like the Van der Pol oscillator
Analyzing stability and equilibrium in chemical or biological dynamical models