Nonlinear Dynamics: A concise introduction interlaced with code

Python package for automated bifurcation analysis and parameter continuations, based on Auto-07p.

Multiscale Modelling Tool - mathematical modelling without the maths

vMatrix-free stability, bifurcation, and sensitivity analysis for incompressible flows using Nek5000

Solving bifurcation problems in elasticity using auto-07p

Continuation methods of Deep Neural Networks optimization, deep-learning, homotopy, bifurcation-analysis, continuation

In this repository, I am working on a framework that contains various methods from equation-free modeling, especially bifurcation analysis and projective integration.

Data and codes supporting the manuscript "Dialogue mechanisms between astrocytic and neuronal networks: a whole-brain modelling approach" by Ali et al., 2025, PCBI.

Code from the study "Ghost channels and ghost cycles guiding long transients in dynamical systems"

An illustration of a few nonlinear dynamical systems solved using Julia-1.1.1.

High-precision bifurcation analysis using Newton's method.

Simulaciones numéricas en módelos de ecuaciones diferenciales

Code and data for Phase-Tunneling Cosmogenesis. Identifies a robust critical mass (mϕ​≃1.965) defining a finite-window 'escape sector'. Demonstrates that time is a transient excursion (Barbour's time capsules) vanishing into asymptotic synchronization, with initial conditions selected via WKB tunneling.

Code and data of the paper Clusella et al. "Complex spatiotemporal oscillations emerge from transverse instabilities in large-scale brain networks" (2023) https://doi.org/10.1371/journal.pcbi.1010781

Builds a self-learning Telegram AI agent that writes code, tracks costs, and adapts from past failures.

Bifurcation Diagram - The Logistic Map, interactive and written in P5JS

Code, phase portraits, and dynamic simulations for the preprint "CREATIVE LOOP: Informational Replication Dynamics and Stability

Raw data and files used to generate plots in the "Shape of a filament on the surface of a bubble" paper (arXiv:2104.09212)

Material de apoyo interactivo para el tema de Teoría de Bifurcaciones.

Developed code using the Hybrid Automata Library (HAL) to create a spatial agent-based model of radio-immune response to spatially fractionated radiotherapy. This project was in association with the Cleveland Clinic Lerner Research Institute, Jacob Scott Lab.