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name: phase-portrait-generator description: Generate phase portraits for 2D dynamical systems. Use when visualizing vector fields, nullclines, and trajectories. version: 1.0.0

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

Copyimport 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