BeClaude

yzmir-simulation-foundations

New
12Community RegistryGeneralby tachyon-beep

Game simulation mathematics - ODEs, stability, control theory - 9 skills

First seen 5/22/2026

Summary

This skill provides expertise in game simulation mathematics, covering ordinary differential equations (ODEs), stability analysis, and control theory.

  • It helps developers model dynamic systems, analyze equilibrium and stability, and design controllers for realistic game physics and simulations.

Overview

Professional AI/ML, Python & Rust engineering, web backend, DevOps, SDLC, solution architecture, game development, security, documentation, and UX skills for Claude Code

44 complete skillpacks • 200+ skills • Install what you need

Recent additions (May 2026): 6 new packs — yzmir-morphogenetic-rl,

axiom-determinism-and-replay, axiom-audit-pipelines,

axiom-static-analysis-engineering, axiom-rust-workspaces,

axiom-pyo3-interop. Plus a 2026-era refresh sweep across the AI/ML cluster

(PyTorch 2.9+, FSDP2, vLLM/SGLang, GRPO/DreamerV3, Mamba/SSM, modern PEFT) and

the design/security/quality packs (WCAG 2.2, Material 3, Pydantic v2,

Typst 0.14, SLSA/SBOM/Sigstore).

In-flight expansions: lyra-creative-writing v0.2 — genre annex with 9

genre sheets (mystery, thriller, sf, fantasy, horror, romance, literary-fiction,

memoir-and-personal-essay, literary-journalism) using a reader-contract

three-move discipline, plus 3 new agents (worldbuilding-consultant,

opening-and-ending-doctor, premise-stress-tester). axiom-system-archaeologist

v1.6 — ultralarge-tier per-module track for repos >100K LOC or >12 subsystems,

with calibration-driven YAML-parse self-validation.


Installation

Via Marketplace (Recommended)

bash
# Add the skillpacks marketplace
/plugin marketplace add tachyon-beep/skillpacks

# Browse available plugins
/plugin

# Install specific packs
/plugin install yzmir-deep-rl
/plugin install lyra-ux-designer
/plugin install ordis-security-architect

Via Git Clone (Development)

bash
git clone https://github.com/tachyon-beep/skillpacks
cd skillpacks
/plugin marketplace add .

Available Skillpacks

Skillpack groupings are inspired by the factions from [Altered TCG](https://www.altered.gg). See [FACTIONS.md](FACTIONS.md) for the philosophical connections between factions and skillpack domains.

🔒 Security (Ordis)

ordis-security-architect - 11 skills, 3 commands, 2 agents _(refreshed for 2026)_

  • Threat modeling (STRIDE / CWE / CVSS / ATT&CK), security controls
  • Compliance: NIST CSF 2.0, ISO 27001:2022, PCI-DSS v4.0.1, GDPR, NIS2, EU AI Act
  • LLM/AI security (OWASP LLM Top 10:2025, MITRE ATLAS), supply-chain

(SLSA, SBOM, Sigstore), ATO/RMF

  • /plugin install ordis-security-architect

📝 Documentation (Muna) - 4 Packs

muna-document-designer - 1 skill, 1 agent, 1 command

  • Professional document design with Pandoc and Typst
  • Typography, layout, templates, branded document systems
  • Reports, proposals, specifications, resumes, brochures
  • /plugin install muna-document-designer

muna-technical-writer - 10 skills, 4 commands, 3 agents

  • Documentation structure, clarity & style, diagram conventions
  • Security-aware docs, incident response, ITIL/governance
  • Includes complex-writer / complex-reviewer agent pair for surgical edits

in large files (≥2000 lines), cross-language

  • /plugin install muna-technical-writer

muna-panel-review - 3 agents, 1 skill, 3 commands

  • Simulated audience panel review with persona-driven editorial intelligence
  • Spawn reader personas, collect mood journals, synthesize cross-panel feedback
  • /plugin install muna-panel-review

muna-wiki-management - 7 skills, 4 commands, 2 agents

  • Document set management as wikis with architecture and governance
  • Derivation tracking, consistency auditing, evolution management
  • /plugin install muna-wiki-management

🔬 Development (Axiom) - 16 Packs

axiom-python-engineering - 10 skills

  • Modern Python 3.13: uv-first tooling, ty/pyrefly, current pre-commit revs
  • Testing, async, debugging, profiling, delinting
  • Scientific computing (NumPy/pandas), ML workflows
  • /plugin install axiom-python-engineering

axiom-rust-engineering - router + 11 reference sheets, 5 commands, 3 agents

  • Rust 2024 edition: ownership, traits, async (tokio), testing
  • Clippy/cargo tooling, performance, unsafe/FFI, AI/ML interop (PyO3, candle)
  • Single-crate-shaped — composes with axiom-rust-workspaces and axiom-pyo3-interop
  • /plugin install axiom-rust-engineering

axiom-rust-workspaces - router + 13 sheets, 3 commands, 1 agent _(new — May 2026)_

  • Rust at workspace scope: multi-crate composition, [workspace.dependencies],

[workspace.lints], deny.toml with waiver lifecycle

  • Feature unification (resolver-2/3), Miri-on-subset, public-vs-internal crate

boundaries (internal-traits-crate / sealed-trait), 10-pattern anti-pattern list

  • /plugin install axiom-rust-workspaces

axiom-pyo3-interop - router + 13 sheets, 3 commands, 1 agent _(new — May 2026)_

  • Python ↔ Rust FFI discipline: Bound<'py, T>, GIL release, abi3, maturin
  • Batched FFI to amortise crossing cost, zero-copy NumPy buffer protocol,

Gymnasium environments backed by Rust, async across the boundary

  • Wheel matrix (cibuildwheel, manylinux), interpreter-teardown discipline
  • /plugin install axiom-pyo3-interop

axiom-system-archaeologist - 5 commands, 4 agents _(v1.6 ultralarge-tier — May 2026)_

  • Deep codebase architecture analysis through subagent coordination
  • C4 diagrams (Context, Container, Component levels), subsystem catalogs,

security surface mapping, test infrastructure analysis, dependency visualization

  • Incremental delta analysis, cross-pack specialist integration
  • Ultralarge-tier per-module track for repos >100K LOC or >12 subsystems, with

calibration-driven YAML-parse self-validation (v1.6.0 + v1.6.1)

  • Stakeholder-ready architecture documentation with output-contract validation gates
  • /plugin install axiom-system-archaeologist

axiom-system-architect - 4 skills

  • TDD-validated architectural assessment with professional discipline
  • Prevents diplomatic softening, analysis paralysis, security compromise
  • Router + 3 specialist skills for technical debt and architecture review
  • /plugin install axiom-system-architect

axiom-solution-architect - 9 skills, 2 agents, 2 commands

  • Forward solution architecture: brief/HLD/epic → traceable artifact set
  • ADRs, C4, NFRs, RTM, integration/migration, risks, TOGAF/ArchiMate
  • Consolidated Solution Architecture Document (SAD) with consistency gate
  • /plugin install axiom-solution-architect

axiom-web-backend - 12 skills

  • FastAPI, Django, Express.js development patterns
  • REST/GraphQL API design, microservices architecture
  • Authentication, database integration, message queues
  • API testing, documentation, production deployment
  • /plugin install axiom-web-backend

axiom-devops-engineering - 1 skill

  • CI/CD pipeline architecture, deployment strategies
  • Zero-downtime deployments, infrastructure reliability
  • /plugin install axiom-devops-engineering

axiom-sdlc-engineering - 8 skills + 4 agents

  • CMMI-based SDLC framework (Levels 2-4) with GitHub/Azure DevOps integration
  • Requirements lifecycle, design/build, quality assurance, governance & risk
  • Platform integration, quantitative management, lifecycle adoption
  • Specialist agents for architecture decisions, bug triage, QA, and process routing
  • /plugin install axiom-sdlc-engineering

axiom-planning - 2 skills, 5 agents, 1 command

  • TDD-validated implementation planning with plan review quality gate
  • Plan review spawns 4 parallel reviewers (reality, architecture, quality, systems) + synthesizer
  • Catches hallucinations, convention violations, and risks before code execution
  • /plugin install axiom-planning

axiom-program-management - router + 13 sheets, 3 commands, 2 agents _(new — June 2026)_

  • Project & program management as a delivery discipline — lean/agile-leaning,

honest about where program scale needs predictive structure

  • Project tier: flow metrics & WIP, scope/backlog control, Monte-Carlo

forecasting, stakeholder management, operational RAID logs, watermelon-resistant status reporting, dependency coordination

  • Program tier: governance, benefits realization & OKRs, now/next/later

roadmapping with WSJF, cross-project dependencies, capacity & stable teams, scaling without framework dogma

  • Leans on axiom-planning (implementation plans) and axiom-sdlc-engineering

(process maturity, traceability, formal governance)

  • /plugin install axiom-program-management

axiom-product-management - router + 8 sheets, 3 commands, 2 agents _(new — June 2026)_

  • Product management as standing ownership — take control of a software

product and own it end-to-end across sessions

  • A git-versioned product workspace (vision, intent-roadmap, Product Decision

Records, current-state, falsifiable metrics) + a resume→decide→dispatch→accept→ checkpoint loop + an authority boundary that escalates anything irreversible

  • Discovery & opportunity, vision/strategy/positioning, PRDs with falsifiable

acceptance criteria, delivery orchestration & acceptance, product-value metrics

  • Orchestrates, doesn't reimplement: routes sequencing/WSJF to

axiom-program-management, plans to axiom-planning, solution design to axiom-solution-architect, research method to lyra-ux-designer

  • /plugin install axiom-product-management

axiom-embedded-database - router + 13 sheets, 3 commands, 2 agents

  • SQLite & DuckDB as application-embedded databases at production scale
  • PRAGMA discipline, migrations under SQLite's ALTER constraints, WAL tuning,

transactions & isolation, single-writer concurrency, optimistic locking

  • Parameterized-SQL enforcement, JSON1, FTS5, DuckDB for OLAP, SQLCipher,

online backup & corruption recovery

  • /plugin install axiom-embedded-database

axiom-procedural-architecture - router + 13 sheets, 3 commands, 2 agents

  • Structural reasoning for staged procedures — design, critique, and analyze

decompositions into composable stages with explicit dependencies, decision points, and flow properties

  • Pattern pack for wizards, troubleshooting trees, training curricula,

configuration flows, decision pipelines, and workflows

  • /plugin install axiom-procedural-architecture

axiom-mcp-engineering - router skill _(early access)_

  • Engineering MCP (Model Context Protocol) servers as production-grade agent

interfaces — tool API surface design, idempotency & atomic claim semantics under agent retry, structured error envelopes, schema versioning, transport reliability

  • /plugin install axiom-mcp-engineering

axiom-engineering-foundations - 6 skills

  • Universal software engineering methodology (language-agnostic)
  • Systematic debugging, safe refactoring, code review, incident response
  • Technical debt triage, codebase confidence building
  • /plugin install axiom-engineering-foundations

axiom-audit-pipelines - router + 11 sheets, 3 commands, 2 agents _(new — May 2026)_

  • Audit-grade decision pipelines: canonical encoding (RFC 8785 JCS), append-only

decision logs, fingerprint chains (linked-hash and Merkle)

  • HMAC and Ed25519 signed exports, immutable storage, decision provenance

(inputs/ruleset/code closure), threat model for the log itself

  • Retention reconciled with right-to-be-forgotten, partial replay, performance budgets
  • /plugin install axiom-audit-pipelines

axiom-determinism-and-replay - router + 13 sheets, 3 commands, 2 agents _(new — May 2026)_

  • Architecture-level determinism and replay for RL substrates, multi-agent

systems, multiplayer lockstep engines, replay-debuggable services

  • Seed governance, RNG isolation, snapshot strategy, divergence detection,

rollback, concurrency strategies, floating-point and GPU determinism

  • External-effects substitution, canonical state encoding, property tests,

cost-of-determinism accounting

  • /plugin install axiom-determinism-and-replay

axiom-static-analysis-engineering - router + 13 sheets, 3 commands, 2 agents _(new — May 2026, v0.2)_

  • Building static analyzers as engines, not running them as users
  • AST visitation, taint-lattice (abstract-domain) design with monotonicity,

three-phase inference (variable → function → callgraph) with termination proofs

  • Plugin architecture for rules, false-positive economics with auditable

suppression lifecycle, the static-vs-runtime boundary

  • Callgraph construction (Rung 0–4 resolution, dynamic-feature handling),

cross-module flow with stub libraries, decorator-as-assertion (runtime + static agreement contract), manifest-driven configuration with coherence validation, SARIF / CI integration, incremental analysis at scale, LLM-assisted finding explanations as a substitutable pattern

  • /plugin install axiom-static-analysis-engineering

🤖 AI/ML Engineering (Yzmir) - 11 Packs

yzmir-ai-engineering-expert - 1 router skill

  • Primary router that directs to specialized AI/ML packs
  • /plugin install yzmir-ai-engineering-expert

yzmir-pytorch-engineering - 9 skills _(refreshed for PyTorch 2.9+)_

  • Tensors, modules, distributed training, profiling, debugging
  • torch.compile, FSDP1/FSDP2, FlexAttention, torch.amp
  • /plugin install yzmir-pytorch-engineering

yzmir-training-optimization - 11 skills _(refreshed)_

  • Modern optimizers, schedules, mixed-precision, batch-size strategy
  • Learning rates, convergence, hyperparameter tuning
  • /plugin install yzmir-training-optimization

yzmir-deep-rl - 13 skills _(refreshed)_

  • DQN, PPO, SAC, reward shaping, exploration
  • Modern offline RL, GRPO, DreamerV3 / TD-MPC2, REDQ/DroQ/CrossQ,

MAPPO/IPPO, BBF/Agent57, Go-Explore

  • /plugin install yzmir-deep-rl

yzmir-morphogenetic-rl - router + 7 sheets, 2 commands, 2 agents _(new — May 2026)_

  • RL controllers that decide WHEN/HOW to mutate a network's topology during training
  • Controller action/observation/reward design, governor and safety gates
  • Rollback-as-RL-signal, deterministic morphogenesis, ablation under topology change
  • Companion to yzmir-dynamic-architectures
  • /plugin install yzmir-morphogenetic-rl

yzmir-neural-architectures - 9 skills _(refreshed)_

  • CNNs, Transformers, RNNs, attention mechanisms, architecture selection
  • Mamba/SSM, MoE (Mixtral/DeepSeek/OLMoE), modern diffusion (SDXL/FLUX/DiT/SD3),

multimodal (CLIP/SigLIP/LLaVA), SAM/SAM-2, ConvNeXt v2, equivariant GNNs

  • /plugin install yzmir-neural-architectures

yzmir-llm-specialist - 8 skills _(refreshed)_

  • Reasoning models, agentic + MCP, modern serving stack, DPO/GRPO
  • RAG with contextual retrieval, fine-tuning, inference optimization
  • /plugin install yzmir-llm-specialist

yzmir-ml-production - 11 skills _(refreshed)_

  • torch.ao.quantization, vLLM/SGLang/TensorRT-LLM serving
  • LLM observability, MLOps, monitoring, debugging
  • /plugin install yzmir-ml-production

yzmir-simulation-foundations - 9 skills

  • Differential equations, stability analysis, control theory (game math)
  • /plugin install yzmir-simulation-foundations

yzmir-systems-thinking - 6 skills

  • Systems thinking methodology, patterns, leverage points
  • Archetypes, modeling, visualization
  • /plugin install yzmir-systems-thinking

yzmir-dynamic-architectures - 6 skills, 1 agent, 2 commands _(refreshed)_

  • Dynamic/morphogenetic neural networks: grow, prune, adapt topology
  • Continual learning, gradient isolation, lifecycle orchestration
  • Modern PEFT (VeRA/PiSSA/LoftQ/LoRA+/rsLoRA/LongLoRA), post-Mixtral MoE,

adapter merging (TIES/DARE/SLERP/MergeKit)

  • /plugin install yzmir-dynamic-architectures

🎮 Game Development (Bravos) - 2 Packs

bravos-simulation-tactics - 11 skills

  • Physics simulation, ecosystem simulation, crowd simulation
  • /plugin install bravos-simulation-tactics

bravos-systems-as-experience - 9 skills

  • Emergent gameplay, player-driven narratives, strategic depth
  • /plugin install bravos-systems-as-experience

🎨 UX, Site Design & Creative Writing (Lyra) - 3 Packs

lyra-creative-writing - 1 router + 13 craft + 9 genre sheets, 3 commands, 11 agents _(v0.2 genre annex — May 2026)_

  • Workshop-voiced craft pack for prose narrative — fiction and creative nonfiction
  • Three explicit modes (draft, critique, plan) with mode-switching protocol
  • Craft coverage: POV and voice, scene construction, dialogue, character interiority,

showing-vs-telling, prose rhythm, pacing and tension, story structure, openings and endings, worldbuilding by implication, research and verisimilitude, revision and cutting, creative nonfiction craft

  • Genre coverage (v0.2): mystery, thriller, sf, fantasy, horror, romance,

literary-fiction, memoir-and-personal-essay, literary-journalism — each presenting conventions through a uniform reader-contract three-move discipline (name the contract → name the cost of breaking → name books worth the cost). Literary fiction is one mode among nine, not the unmarked default

  • /critique-prose fans out 5 coach-mode agents in parallel and synthesises a

prioritised revision-pass plan via revision-coach

  • v0.2 agents: worldbuilding-consultant (world abstraction), opening-and-ending-doctor

(promise-ledger output, first-5/last-5 pages), premise-stress-tester (adversarial pre-outline interrogation)

  • Composes with muna-panel-review for beta-reader simulation
  • /plugin install lyra-creative-writing

lyra-site-designer - 1 skill, 1 agent, 1 command, 6 reference sheets

  • Static site design for developer tools and documentation sites
  • Information architecture, HTML/CSS craftsmanship, design tokens
  • Developer UX patterns: code blocks, dark mode, search, responsive layouts
  • Static site tooling guidance (Hugo, Astro, Eleventy)
  • /plugin install lyra-site-designer

lyra-ux-designer - 12 reference sheets _(refreshed for 2026)_

  • WCAG 2.2 accessibility, modern web platform primitives (dialog, popover,

:has(), container queries)

  • iOS 17+ and Material 3 mobile patterns, AI-experience patterns
  • /plugin install lyra-ux-designer

✅ Quality Engineering (Ordis)

ordis-quality-engineering - 21 skills

  • E2E testing, API testing, integration testing, performance testing
  • Chaos engineering, flaky test diagnosis, mutation testing
  • Observability, test automation architecture, coverage gap analysis
  • /plugin install ordis-quality-engineering

🛠️ Meta Packs

meta-sme-protocol - 1 skill

  • SME (Subject Matter Expert) Agent Protocol
  • Mandatory protocol for all specialist agents: fact-finding, confidence/risk assessment
  • /plugin install meta-sme-protocol

meta-skillpack-maintenance - 3 skills

  • Systematic maintenance and enhancement of skill packs
  • Investigative domain analysis, RED-GREEN-REFACTOR testing
  • Automated quality improvements
  • /plugin install meta-skillpack-maintenance

Quick Examples

AI/ML Engineering

bash
/plugin install yzmir-deep-rl
/deep-rl  # Use slash command to load router skill

Claude will guide you to the right specialized skill:

plaintext
I'm using yzmir/deep-rl/policy-gradient-methods to implement PPO for continuous character control

Web Backend Development

bash
/plugin install axiom-web-backend
/web-backend  # Use slash command to load router
plaintext
I'm using axiom/web-backend/fastapi-development to build production-ready async APIs with dependency injection

Game Development

bash
/plugin install bravos-systems-as-experience
/systems-as-experience  # Use slash command to load router
plaintext
I'm using bravos/systems-as-experience/emergent-gameplay-design to create systemic interactions in my RPG

Security Architecture

bash
/plugin install ordis-security-architect
/security-architect  # Use slash command to load router
code
I'm using ordis/security-architect/threat-modeling to analyze this authentication system with STRIDE

UX Design

bash
/plugin install lyra-ux-designer
/ux-designer  # Use slash command to load router
code
I'm using lyra/ux-designer/accessibility-and-inclusive-design to ensure WCAG 2.1 AA compliance

Architecture Analysis

bash
/plugin install axiom-system-archaeologist
/system-archaeologist  # Use slash command to load router
plaintext
Then Claude routes you to specialized analysis skills for C4 diagrams, subsystem catalogs, etc.

Using Router Skills: Slash Commands vs Direct Invocation

Slash Commands (Recommended)

All router skills (using-X skills) are available as slash commands to avoid skill context limits:

bash
/ai-engineering          # Route to AI/ML specialized packs
/deep-rl                # Route to RL algorithm skills
/system-archaeologist   # Route to architecture analysis
/python-engineering     # Route to Python skills
/web-backend           # Route to web backend skills
/ux-designer           # Route to UX design skills
# ... and 12 more

Why slash commands? Router skills are comprehensive guides that exceeded the context budget for automatic skill discovery. Slash commands provide explicit, user-controlled invocation without context limits.

See `.claude/SLASH_COMMANDS.md` for the complete list of all router commands.

Direct Skill Invocation

If you have only a few plugins installed, direct skill invocation still works:

plaintext
I'm using yzmir/deep-rl/policy-gradient-methods to implement PPO

Caveat: With many plugins installed (5+), you may hit skill discovery context limits. In this case, use slash commands for routers and direct invocation for specialized skills.

Best Practice:

  • Use slash commands for router skills (/ai-engineering, /deep-rl, etc.)
  • Use direct invocation for specialized skills after the router guides you

What's Inside

  • 200+ Skills: Production-ready guidance across 7 domains
  • 38 Packs: Install only what you need
  • Per-Pack Plugins: Independent versioning, clean dependencies
  • Complete Coverage: Design → Foundation → Training → Production

Repository Structure

code
skillpacks/
├── .claude-plugin/
│   └── marketplace.json       # Marketplace catalog
├── plugins/                   # All 38 skillpacks
│   ├── axiom-*/               # Development (15 packs)
│   ├── bravos-*/              # Game development (2 packs)
│   ├── lyra-*/                # UX & site design (2 packs)
│   ├── meta-*/                # Meta utilities (2 packs)
│   ├── muna-*/                # Documentation (4 packs)
│   ├── ordis-*/               # Quality & security (2 packs)
│   └── yzmir-*/               # AI/ML (11 packs)
└── docs/                      # Planning documents

Contributing

See CONTRIBUTING.md for guidelines on adding skills or creating new packs.


License

CC BY-SA 4.0 (Creative Commons Attribution-ShareAlike 4.0 International) - See LICENSE for details.

Note: Faction names (Axiom, Bravos, Lyra, Muna, Ordis, Yzmir) from Altered TCG are NOT covered by this license - see LICENSE_ADDENDUM.md.


About

Built by @tachyon-beep

Skillpacks provides modular, production-ready expertise for Claude Code across professional domains. Each skillpack is independently versioned and installable, containing systematically validated skills that guide Claude through expert-level implementations.

Install & Usage

1
Open your MCP config
~/.claude.json
2
Add the server config

Add the configuration to "mcpServers": { "yzmir-simulation-foundations": { "command": "...", "args": [] } }

3
Restart Claude Code
/mcp

Use Cases

Implement numerical integration of ODEs for physics-based character movement or projectile trajectories.
Analyze the stability of a game's economy or resource system using linear stability analysis.
Design a PID controller for an autonomous vehicle or drone in a simulation environment.
Model predator-prey dynamics or population growth in a strategy game using differential equations.
Simulate spring-mass-damper systems for realistic vehicle suspension or cloth physics.
Validate control system performance through phase portraits and bifurcation analysis.

Usage Examples

1

/yzmir-simulation-foundations Implement a Runge-Kutta 4th order integrator for a 3D projectile with air resistance.

2

Model a simple pendulum with damping and plot its phase portrait using ODE solvers.

3

Design a LQR controller for a quadcopter simulation and test its stability under disturbances.

View source on GitHub
yzmirsimulationfoundations

Security Audits

LicenseUnknownSourceWarnRepositoryPass

Frequently Asked Questions

What is yzmir-simulation-foundations?

This skill provides expertise in game simulation mathematics, covering ordinary differential equations (ODEs), stability analysis, and control theory. It helps developers model dynamic systems, analyze equilibrium and stability, and design controllers for realistic game physics and simulations.

How to install yzmir-simulation-foundations?

To install yzmir-simulation-foundations: open your mcp config (~/.claude.json), then add the config to "mcpServers": { "yzmir-simulation-foundations": { "command": "...", "args": [] } }. Finally, /mcp in Claude Code.

What is yzmir-simulation-foundations best for?

yzmir-simulation-foundations is a mcp categorized under General. It is designed for: yzmir, simulation, foundations. Created by tachyon-beep.

What can I use yzmir-simulation-foundations for?

yzmir-simulation-foundations is useful for: Implement numerical integration of ODEs for physics-based character movement or projectile trajectories.; Analyze the stability of a game's economy or resource system using linear stability analysis.; Design a PID controller for an autonomous vehicle or drone in a simulation environment.; Model predator-prey dynamics or population growth in a strategy game using differential equations.; Simulate spring-mass-damper systems for realistic vehicle suspension or cloth physics.; Validate control system performance through phase portraits and bifurcation analysis..