Nonlinear Dynamical Systems — Scientific Machine Learning & Regime Shifts

Research-grade computational studies of nonlinear dynamical systems focused on:

• Stability and attractor structure
• Predictability limits (chaos, noise, sensitivity)
• Regime behavior and critical transitions
• Equation-based simulation combined with data-driven analysis

This repository is methods-first: each study is organized around transferable tools for simulation, parameter sweeps, stability diagnostics, and regime-shift detection.

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Start Here (Flagship Project)

If you only look at one thing in this repository, start with the flagship study:

Tri-Trophic Regime Shifts and Early-Warning Detection

📁 ecology/tritrophic-early-warning/

This project implements an end-to-end, reproducible pipeline to:

• Simulate nonlinear tri-trophic population dynamics
• Analyze attractor geometry and long-run behavior
• Quantify predictability collapse approaching regime transitions
• Evaluate early-warning indicators directly from time series (equation-free)

Quickstart (Reproduce One Main Result)

git clone https://github.com/OussamaNajar/nonlinear-dynamical-systems.git
cd nonlinear-dynamical-systems/ecology/tritrophic-early-warning
Rscript scripts/run_pipeline.R

Runtime: ~3-4 minutes
Dependencies: R (≥4.1) + deSolve package only

Key Results (Summary)

• Predictability horizon collapses as the system approaches a regime transition
• Early-warning indicators rise consistently prior to critical transitions across parameter sweeps
• Results are robust to noise and perturbations within tested regimes

➡️ Full technical documentation, assumptions, and reproduction details:
ecology/tritrophic-early-warning/README.md

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Why This Matters

Many real systems — ecosystems, markets, climate, engineered control loops — share the same fundamental difficulties:

• Nonlinear feedback produces multi-regime behavior
• Prediction skill degrades sharply beyond a horizon
• Regime change dominates error more than model misspecification
• Better curve-fitting does not imply greater predictability

This repository is built to answer a concrete question:

What aspects of a nonlinear system are structurally predictable, what are not, and why?

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Repository Structure

nonlinear-dynamical-systems/
├── ecology/
│   └── tritrophic-early-warning/
│       ├── README.md        # full technical documentation
│       ├── scripts/         # runnable analysis entrypoints
│       ├── R/               # modular functions
│       ├── results/         # generated outputs
│       ├── figures/         # generated plots
│       └── paper/           # manuscript-quality writeup

Each study directory is self-contained and includes:

• Runnable code (R/, src/, or scripts/)
• Generated outputs and figures
• Explicit reproduction instructions
• Documented assumptions and interpretation

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Featured Study: Tri-Trophic Ecological Dynamics

Hastings–Powell Family

A computational study of nonlinear tri-trophic food-chain models emphasizing:

• Attractor geometry and long-run dynamics
• Parameter sensitivity and regime transitions
• Predictability limits under perturbations
• Interpretation in a management/decision-making context

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Reproducibility

All figures and results are generated from code. No manual post-processing is required.

Each study directory contains its own README.md with:

• Environment requirements
• Step-by-step execution instructions
• Expected outputs and diagnostics

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Notes for Reviewers and Recruiters

This repository is organized to reflect research and modeling workflows, not coursework.

Emphasis is placed on stability, predictability, and failure modes, not just fitting accuracy.

The flagship project demonstrates the full pipeline from simulation → diagnostics → interpretation.

For a technical deep dive, start with:
ecology/tritrophic-early-warning/README.md