# Phase Portrait Generator

> Generate phase portraits for 2D dynamical systems. Use when visualizing vector fields, nullclines, and trajectories.

- Skill: `plurigrid/phase-portrait-generator` (Agent Skill, multi-file: 2 files)
- Install (CLI): `npx skillmds@latest add plurigrid/phase-portrait-generator`
- Raw SKILL.md: https://api.skillmd.com/api/skills/plurigrid/phase-portrait-generator/raw
- Safety review: pending
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: Coding & Dev Tools
- Author: plurigrid (https://skillmd.com/u/plurigrid)
- Updated: 2026-09-17
- Page: https://skillmd.com/skills/plurigrid/phase-portrait-generator

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# Phase Portrait Generator

Generates phase portraits showing vector fields and trajectories in 2D state space.

## When to Use
- Visualizing 2D autonomous systems
- Plotting nullclines and equilibria
- Trajectory analysis in phase space

## GF(3) Role
PLUS (+1) Generator - creates visual outputs from differential equations.

## Quick Example

```python
import numpy as np
import matplotlib.pyplot as plt

def phase_portrait(f, xlim=(-3,3), ylim=(-3,3), density=20):
    x = np.linspace(*xlim, density)
    y = np.linspace(*ylim, density)
    X, Y = np.meshgrid(x, y)
    U, V = f(X, Y)
    plt.streamplot(X, Y, U, V, density=1.5)
    plt.xlabel('x'); plt.ylabel('y')

# Van der Pol oscillator
phase_portrait(lambda x, y: (y, -x + (1 - x**2) * y))
```

## Integration with bifurcation skills

Forms triad with:
- `bifurcation` (0): detects transitions
- `bifurcation-generator` (+1): parameter space
- `phase-portrait-generator` (+1): state space