kuramoto-model
Coupled oscillators with sinusoidal coupling
Best use case
kuramoto-model is best used when you need a repeatable AI agent workflow instead of a one-off prompt.
Coupled oscillators with sinusoidal coupling
Teams using kuramoto-model should expect a more consistent output, faster repeated execution, less prompt rewriting.
When to use this skill
- You want a reusable workflow that can be run more than once with consistent structure.
When not to use this skill
- You only need a quick one-off answer and do not need a reusable workflow.
- You cannot install or maintain the underlying files, dependencies, or repository context.
Installation
Claude Code / Cursor / Codex
Manual Installation
- Download SKILL.md from GitHub
- Place it in
.claude/skills/kuramoto-model/SKILL.mdinside your project - Restart your AI agent — it will auto-discover the skill
How kuramoto-model Compares
| Feature / Agent | kuramoto-model | Standard Approach |
|---|---|---|
| Platform Support | Not specified | Limited / Varies |
| Context Awareness | High | Baseline |
| Installation Complexity | Unknown | N/A |
Frequently Asked Questions
What does this skill do?
Coupled oscillators with sinusoidal coupling
Where can I find the source code?
You can find the source code on GitHub using the link provided at the top of the page.
SKILL.md Source
# Kuramoto Model
**Trit**: 1 (PLUS)
**Domain**: Dynamical Systems Theory
**Principle**: Coupled oscillators with sinusoidal coupling
## Overview
Kuramoto Model is a fundamental concept in dynamical systems theory, providing tools for understanding the qualitative behavior of differential equations and flows on manifolds.
## Mathematical Definition
```
KURAMOTO_MODEL: Phase space × Time → Phase space
```
## Key Properties
1. **Local behavior**: Analysis near equilibria and invariant sets
2. **Global structure**: Long-term dynamics and limit sets
3. **Bifurcations**: Parameter-dependent qualitative changes
4. **Stability**: Robustness under perturbation
## Integration with GF(3)
This skill participates in triadic composition:
- **Trit 1** (PLUS): Sources/generators
- **Conservation**: Σ trits ≡ 0 (mod 3) across skill triplets
## AlgebraicDynamics.jl Connection
```julia
using AlgebraicDynamics
# Kuramoto Model as compositional dynamical system
# Implements oapply for resource-sharing machines
```
## Related Skills
- equilibrium (trit 0)
- stability (trit +1)
- bifurcation (trit +1)
- attractor (trit +1)
- lyapunov-function (trit -1)
---
**Skill Name**: kuramoto-model
**Type**: Dynamical Systems / Kuramoto Model
**Trit**: 1 (PLUS)
**GF(3)**: Conserved in triplet composition
## Non-Backtracking Geodesic Qualification
**Condition**: μ(n) ≠ 0 (Möbius squarefree)
This skill is qualified for non-backtracking geodesic traversal:
1. **Prime Path**: No state revisited in skill invocation chain
2. **Möbius Filter**: Composite paths (backtracking) cancel via μ-inversion
3. **GF(3) Conservation**: Trit sum ≡ 0 (mod 3) across skill triplets
4. **Spectral Gap**: Ramanujan bound λ₂ ≤ 2√(k-1) for k-regular expansion
```
Geodesic Invariant:
∀ path P: backtrack(P) = ∅ ⟹ μ(|P|) ≠ 0
Möbius Inversion:
f(n) = Σ_{d|n} g(d) ⟹ g(n) = Σ_{d|n} μ(n/d) f(d)
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