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bifurcation-generator

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Bifurcation Generator

分岔图生成器

Generates bifurcation diagrams showing how system behavior changes with parameters.
为动力系统生成分岔图，展示系统行为如何随参数变化。

When to Use

使用场景

  • Visualizing Hopf, pitchfork, saddle-node bifurcations
  • Parameter sweeps in dynamical systems
  • Stability boundary identification
  • 可视化Hopf分岔、叉形分岔、鞍结分岔
  • 动力系统中的参数扫描
  • 稳定性边界识别

GF(3) Role

GF(3) 角色

PLUS (+1) Generator - creates visual outputs from system parameters.
PLUS (+1) 生成器 - 根据系统参数创建可视化输出。

Quick Examples

快速示例

python
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python
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Logistic map bifurcation

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
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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
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Integration with bifurcation (0) skill

与bifurcation（0级）技能集成

This skill (PLUS +1) pairs with 
bifurcation
(ERGODIC 0) for balanced analysis:
  • bifurcation: detects and classifies transitions
  • bifurcation-generator: visualizes parameter space
此技能（PLUS +1）可与
bifurcation
（ERGODIC 0）配合使用，实现均衡分析：
  • bifurcation：检测并分类转变
  • bifurcation-generator：可视化参数空间