r-irbe General Nonlinear Dynamics & Catastrophe Theory
Comprehensive mathematical methodology for nonlinear dynamics — the theoretical backbone of phase portraits, catastrophe models, Lyapunov stability, and governance convergence modules.
Routing
- USE FOR: General nonlinear dynamics, chaos theory, bifurcation analysis, catastrophe theory, attractor geometry, Lyapunov methods, phase portraits, and control-theoretic stability. Use for any mathematical reasoning about dynamical systems BEFORE or BEYOND Lean formalization. Covers theory, intuition, calculation techniques, and connections to phase portraits, catastrophe models, and governance dynamics.
- DO NOT USE FOR: Lean proofs in this domain (use @lean-math-dynamical); optimization theory (use @math-optimization-game); topology methods (use @math-topology-analysis).
- TRIGGERS: nonlinear dynamics, chaos theory, bifurcation, catastrophe theory, attractor, Lyapunov, phase portrait.
Workflow
- Classify the system: ODE / PDE / map / SDE / hybrid; identify the phase-space and invariants.
- Pick the matching section (Lyapunov / bifurcation / catastrophe / chaos / control).
- Produce the answer with explicit assumptions + regularity; cite the Mathlib namespace if applicable.
- Hand off: to
@lean-math-dynamicalfor the Lean proof, to@math-optimization-gameif control becomes optimal-control, to@lean-zettelkasten.
Recovery & STOP
- STOP if the question is about optimisation (not dynamics) — delegate to
@math-optimization-game. - STOP if topological tools dominate — delegate to
@math-topology-analysis. - STOP if Mathlib lacks the needed lemma — escalate to
@lean-research.
Handoffs
- Predecessors:
agent:gateway,skill:lean-research. - Successors:
skill:lean-math-dynamical,skill:lean-research,skill:lean-zettelkasten.
Detailed reference
Full content for math-nonlinear-dynamics lives in
references/math-nonlinear-dynamics-handbook.md.
Load that file when the skill is convened; the SKILL.md only carries
the dispatch contract and the parts index.
| Section | Topic |
|---|---|
| Part 1 | Core Mathematical Framework |
| Part 2 | Bifurcation Analysis Methodology |
| Part 3 | Lyapunov Function Construction |
| Part 4 | Phase Portrait Analysis |
| Part 5 | Control-Theoretic Perspective |
| Part 6 | Connections to Other Mathematical Disciplines |
| Part 7 | Research Entry Points |
See also
../../references/math-nonlinear-dynamics-handbook.md— Full handbook (extracted from this skill)../lean-math-dynamical/SKILL.md— Successor../lean-research/SKILL.md— Successor../lean-zettelkasten/SKILL.md— Successor