Nonlinear Dynamics: A concise introduction interlaced with code

Multiscale Modelling Tool - mathematical modelling without the maths

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

Matrix-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.

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

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

High-precision bifurcation analysis using Newton's method.

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

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

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.

Modelling of a coupled reactor-separator system with transport delay

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

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

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

Created code to develop and analyze statistical graphs for the spatial radiotherapy model, which can be found at https://github.com/hannahgsimon/HALModeling2024. This project was in association with the Cleveland Clinic Lerner Research Institute, Jacob Scott Lab.

🎸 Revival of Classic Academic Simulators in Rust - GENESIS, NEURON, XPPAUT, AUTO, COPASI, Brian, NEST

Interactive nonlinear dynamics simulator with Lyapunov spectrum, Poincare sweeps, continuation workflows, and Numba acceleration.

Julia implementation of "Quantitative modeling of the terminal differentiation of B cells and mechanisms of lymphomagenesis" by Martinez 2012 (https://doi.org/10.1073/pnas.1113019109)

Repository for the Phase-Bifurcation Cosmogenesis model. Includes, academic paper, reproducible Δϕ simulations, numerical scripts, critical-mass analysis (mϕ,crit ≈ 1.965), and visualizations of a non-singular CPT-symmetric cosmic origin.

Collection of code and manuscripts of my projects in research

Julia and Auto-07p codes for the paper "From chimeras to extensive chaos in networks of heterogeneous Kuramoto oscillator populations", by Pol Floriach, Jordi Garcia-Ojalvo, and Pau Clusella.