bifurcation
Hopf bifurcation detection for dynamical system state transitions with GF(3) phase portraits
npx skills add majiayu000/claude-skill-registry --skill bifurcation-plurigrid-asi --agent claude-code
Same command for any agent — swap --agent for codex, cursor, copilot.
Weekly change comes from our own snapshots, not the repository page — it measures attention, not adoption.
# Bifurcation **Detects and navigates bifurcation points in dynamical systems where qualitative behavior changes.** **Trit**: 0 (ERGODIC - Coordinator between stable states) **Color**: #9966FF (Purple - neutral zone bridging warm/cold) --- ## Core Concepts ### Bifurcation Types | Type | Description | GF(3) Mapping | |------|-------------|---------------| | **Saddle-Node** | Two equilibria collide and annihilate | PLUS ↔ MINUS collision | | **Hopf** | Equilibrium → limit cycle | ERGODIC spawns oscillation | | **Pitchfork** | Symmetry-breaking | One ERGODIC → two ±PLUS/MINUS | | **Transcritical** | Exchange of stability | PLUS ↔ MINUS swap roles | | **Period-Doubling** | Route to chaos | Trit cascade: 0 → 1 → -1 → 0... | --- ## Hopf Bifurcation Detection ```python import numpy as np from scipy.linalg import eig def detect_hopf(jacobian_fn, params, param_name, param_range): """ Detect Hopf bifurcation by finding where eigenvalues cross imaginary axis. At Hopf bifurcation: - Pair of complex conjugate eigenvalues - Real part crosses zero - Imaginary part nonzero (oscillation frequency) """ bifurcation_points = [] for p in param_range: params[param_name] = p J = jacobian_fn(params) eigen
- Core Concepts
- Bifurcation Types
- Hopf Bifurcation Detection
- GF(3) Phase Portrait
- Bifurcation Diagram Generator
- State Transition Detection
- Triadic Bifurcation Analysis
- Integration with ruler-maximal
- Commands
- References
- Related Skills
Analyze system for bifurcations bb -e '(bifurcation/analyze system params)' Generate bifurcation diagram bb scripts/bifurcation_diagram.bb --param r --range "2.5:4.0:0.001" Monitor real-time state transitions bb scripts/bifurcation_monitor.bb --system lorenz
What does the bifurcation skill do?
Hopf bifurcation detection for dynamical system state transitions with GF(3) phase portraits
How do I install it?
Run `npx skills add majiayu000/claude-skill-registry --skill bifurcation-plurigrid-asi --agent claude-code` — it drops the skill into your project so the agent can pick it up. Swap the --agent value for codex, cursor or copilot if you use one of those.
Where does this skill come from?
From majiayu000/claude-skill-registry, a repository with 534 stars. We read it straight from the repository tree rather than a submitted listing, so what you see here is what is actually published.
Is a popular skill a good skill?
Not necessarily. Stars measure attention, not adoption — a repository can trend for a week and be abandoned. That is why we show the weekly change from our own snapshots next to the total, instead of a single flattering number.