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Analyzes stability in dynamical systems using Lyapunov's direct method for equilibria, invariant sets, bifurcations, and perturbation robustness. Includes GF(3) integration and Julia examples.
How this skill is triggered — by the user, by Claude, or both
Slash command
/asi:lyapunov-stabilityThe summary Claude sees in its skill listing — used to decide when to auto-load this skill
**Trit**: 0 (ERGODIC)
Trit: 0 (ERGODIC) Domain: Dynamical Systems Theory Principle: Stability via Lyapunov's direct method
Lyapunov Stability is a fundamental concept in dynamical systems theory, providing tools for understanding the qualitative behavior of differential equations and flows on manifolds.
LYAPUNOV_STABILITY: Phase space × Time → Phase space
This skill participates in triadic composition:
using AlgebraicDynamics
# Lyapunov Stability as compositional dynamical system
# Implements oapply for resource-sharing machines
Skill Name: lyapunov-stability Type: Dynamical Systems / Lyapunov Stability Trit: 0 (ERGODIC) GF(3): Conserved in triplet composition
Condition: μ(n) ≠ 0 (Möbius squarefree)
This skill is qualified for non-backtracking geodesic traversal:
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)
npx claudepluginhub plurigrid/asi --plugin asiExplains Lyapunov functions for stability analysis in dynamical systems theory, including properties, bifurcations, and Julia AlgebraicDynamics integration. Useful for modeling differential equations.
Creates, edits, and optimizes skills for Claude Code, including drafting, evaluating with test prompts, iterating on performance, and improving skill descriptions for better triggering accuracy.