plurigrid 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
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 transitionsbifurcation-generator(+1): parameter spacephase-portrait-generator(+1): state space