Bifurcation Generator
by plurigrid
Generate bifurcation diagrams for dynamical systems. Use when visualizing parameter-dependent behavior transitions.
Skill Details
Repository Files
1 file in this skill directory
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.
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