Explains parameter-dependent systems in dynamical systems theory, including bifurcations, stability, local/global behavior, and Julia AlgebraicDynamics.jl integration. Useful for math modeling with varying parameters.
From asi-skillsnpx claudepluginhub plurigrid/asiThis skill uses the workspace's default tool permissions.
Guides Next.js Cache Components and Partial Prerendering (PPR) with cacheComponents enabled. Implements 'use cache', cacheLife(), cacheTag(), revalidateTag(), static/dynamic optimization, and cache debugging.
Migrates code, prompts, and API calls from Claude Sonnet 4.0/4.5 or Opus 4.1 to Opus 4.5, updating model strings on Anthropic, AWS, GCP, Azure platforms.
Facilitates interactive brainstorming sessions using diverse creative techniques and ideation methods. Activates when users say 'help me brainstorm' or 'help me ideate'.
Trit: 0 (ERGODIC) Domain: Dynamical Systems Theory Principle: Systems varying with external parameters
Parameter-dependent is a fundamental concept in dynamical systems theory, providing tools for understanding the qualitative behavior of differential equations and flows on manifolds.
PARAMETER-DEPENDENT: Phase space × Time → Phase space
This skill participates in triadic composition:
using AlgebraicDynamics
# Parameter-dependent as compositional dynamical system
# Implements oapply for resource-sharing machines
Skill Name: parameter-dependent Type: Dynamical Systems / Parameter-dependent 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)