How does GF(3) logic enhance phase portrait analysis?

GF(3) logic maps system behaviors into three trits: PLUS (+1) for expanding complexity, ERGODIC (0) for neutral cycles, and MINUS (-1) for contracting stability, providing a structured way to visualize state transitions.

What types of bifurcations can this skill detect?

It can detect several major types, including Saddle-Node, Hopf, Pitchfork, Transcritical, and Period-Doubling bifurcations.

What is the primary purpose of the Bifurcation skill?

The skill is designed to detect and navigate points in dynamical systems where the qualitative behavior changes, such as moving from a stable state to an oscillating or chaotic state.

Can I use this for real-time monitoring?

Yes, the skill includes a BifurcationMonitor class that tracks system history and variance to classify regimes and trigger events when a bifurcation occurs.

What programming languages does this skill support?

The skill provides implementation patterns in Python for numerical analysis and Clojure (Babashka) for scripting and diagram generation.

Bifurcation Analysis

Name: Bifurcation Analysis
Author: plurigrid

byplurigrid

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数据科学与机器学习

Detects and analyzes qualitative state transitions in dynamical systems using Hopf bifurcation detection and GF(3) phase portraits.

关于

This skill provides specialized tools for identifying critical transition points in nonlinear systems where small parameter changes lead to sudden qualitative shifts in behavior. By leveraging GF(3) (triadic) logic to classify states as stable (Minus), periodic (Ergodic), or chaotic (Plus), it enables advanced detection of Hopf bifurcations, period-doubling cascades, and symmetry-breaking events. It is an essential capability for researchers and engineers working with complex systems, control theory, or mathematical modeling who need to monitor real-time regime changes and map the stability of complex attractors.

主要功能

Real-time state transition monitoring to identify regime changes
Triadic analysis framework for balanced system exploration using Plus, Ergodic, and Minus agents
Bifurcation diagram generation for mapping the route to chaos
GF(3) phase portrait generation with triadic behavior color-coding
Automated Hopf bifurcation detection via eigenvalue crossing analysis
2 GitHub stars

使用场景

Predicting sudden shifts in population dynamics or financial market stability models
Designing control systems for engineering hardware to maintain stability and avoid chaotic regimes
Visualizing and classifying complex attractors and phase portraits in nonlinear physics research

关于

主要功能

Real-time state transition monitoring to identify regime changes
Triadic analysis framework for balanced system exploration using Plus, Ergodic, and Minus agents
Bifurcation diagram generation for mapping the route to chaos
GF(3) phase portrait generation with triadic behavior color-coding
Automated Hopf bifurcation detection via eigenvalue crossing analysis
2 GitHub stars

使用场景

Predicting sudden shifts in population dynamics or financial market stability models
Designing control systems for engineering hardware to maintain stability and avoid chaotic regimes
Visualizing and classifying complex attractors and phase portraits in nonlinear physics research