name: bifurcation-generator description: Generate bifurcation diagrams for dynamical systems. Use when visualizing parameter-dependent behavior transitions. version: 1.0.0

Bifurcation Generator

Generates bifurcation diagrams showing how system behavior changes with parameters.

When to Use

• Visualizing Hopf, pitchfork, saddle-node bifurcations
• Parameter sweeps in dynamical systems
• Stability boundary identification

GF(3) Role

PLUS (+1) Generator - creates visual outputs from system parameters.

Quick Examples

# Logistic map bifurcation
import numpy as np
import matplotlib.pyplot as plt

def logistic_bifurcation(r_min=2.5, r_max=4.0, steps=1000):
    r_vals = np.linspace(r_min, r_max, steps)
    x = 0.5
    for r in r_vals:
        for _ in range(100):  # transient
            x = r * x * (1 - x)
        for _ in range(50):   # attractor
            x = r * x * (1 - x)
            yield r, x

Integration with bifurcation (0) skill

This skill (PLUS +1) pairs with bifurcation (ERGODIC 0) for balanced analysis:

• bifurcation: detects and classifies transitions
• bifurcation-generator: visualizes parameter space

SDF Interleaving

This skill connects to Software Design for Flexibility (Hanson & Sussman, 2021):

Primary Chapter: 2. Domain-Specific Languages

Concepts: DSL, wrapper, pattern-directed, embedding

GF(3) Balanced Triad

bifurcation-generator (+) + SDF.Ch2 (−) + [balancer] (○) = 0

Skill Trit: 1 (PLUS - generation)

Connection Pattern

DSLs embed domain knowledge. This skill defines domain-specific operations.