How does the GF(3) mapping improve phase portraits?

GF(3) mapping classifies local behavior into three distinct trits: PLUS (+1) for expanding/generating, ERGODIC (0) for neutral/cycling, and MINUS (-1) for contracting/validating, providing a standardized triadic logic for complex system visualization.

What is a bifurcation in the context of this skill?

A bifurcation occurs when a small smooth change made to the parameter values (the bifurcation parameters) of a system causes a sudden qualitative or topological change in its behavior, such as moving from a steady state to an oscillation.

Does this skill help with chaos theory analysis?

Absolutely. It specifically includes tools for detecting period-doubling cascades, which are a primary route to chaotic behavior in systems like the logistic map.

Can this skill monitor systems in real-time?

Yes, the skill includes a BifurcationMonitor class that tracks state history, calculates variance, and detects regime changes (fixed point, limit cycle, or chaotic) as they happen.

Which mathematical frameworks are compatible with this tool?

It is compatible with any dynamical system that can be expressed as a Jacobian function in Python or as a mapping function in Clojure/Babashka.

Bifurcation Analysis Skill | Claude Code Dynamical Systems

The Bifurcation skill provides a sophisticated framework for navigating and identifying state transitions within complex dynamical systems. It enables users to detect Hopf bifurcations where equilibria transform into limit cycles, using eigenvalue analysis to pinpoint critical parameter values. By implementing GF(3) triadic logic, the skill maps system behaviors into stable (MINUS), oscillating (ERGODIC), and expanding (PLUS) states, providing unique topological insights. This tool is ideal for researchers and engineers modeling non-linear systems who need to automate regime detection, generate bifurcation diagrams, and monitor stability boundaries in real-time.

主な機能

01GF(3) phase portrait generation with triadic color-coded behavior mapping

02Bifurcation diagram generation for multi-parameter space exploration

03Real-time state transition monitoring for fixed-point, cyclic, and chaotic regimes

04Multi-agent triadic analysis (PLUS, ERGODIC, MINUS) for parallel system monitoring

05Automated Hopf bifurcation detection via Jacobian eigenvalue analysis

068 GitHub stars

ユースケース

01Monitoring autonomous control systems for transitions from stability to chaos

02Visualizing regime changes in topological simulation environments

03Identifying stability boundaries in biological or chemical oscillation models

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi bifurcation

For use in Claude.ai and ChatGPT

Download Skill

主な機能

01GF(3) phase portrait generation with triadic color-coded behavior mapping

02Bifurcation diagram generation for multi-parameter space exploration

03Real-time state transition monitoring for fixed-point, cyclic, and chaotic regimes

04Multi-agent triadic analysis (PLUS, ERGODIC, MINUS) for parallel system monitoring

05Automated Hopf bifurcation detection via Jacobian eigenvalue analysis

068 GitHub stars

ユースケース

01Monitoring autonomous control systems for transitions from stability to chaos

02Visualizing regime changes in topological simulation environments

03Identifying stability boundaries in biological or chemical oscillation models

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi bifurcation

For use in Claude.ai and ChatGPT

Download Skill

Bifurcation Analysis & State Transitions

Bifurcation Analysis & State Transitions

主な機能

ユースケース

主な機能

ユースケース