bifurcation-analysis

Nonlinear Dynamics: A concise introduction interlaced with code

Stability, bifurcation, and sensitivity analysis for Nek5000

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

Multiscale Modelling Tool - mathematical modelling without the maths

Interactive Research Workstation for Waddington Epigenetic Landscapes, Nonlinear GRN Dynamics, Stochastic Simulation, and Flow Cytometry (FACS) Gating in Rust.

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.

Simulaciones numéricas en módelos de ecuaciones diferenciales

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

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

High-precision bifurcation analysis using Newton's method.

MAT244 final project: modeling calm/turbulent volatility regimes in US equity markets as saddle-node bifurcations of a nonlinear ODE

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.

Non-smooth impact phenomenon in a harmonic oscillator. The system in consideration is a Spring-loaded Bouncing Ball model.

Reduced box model of Atlantic overturning hysteresis with an Indo-Pacific gateway: exact fold and cusp structure, a salt-conservation identity constraining gateway influence, and distributed-memory Hopf thresholds.

A dynamical-systems framework for compositional generalisation failure

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