Projects

Publications

Patiño-Echeverría, Krauskopf & Osinga (2026) Global bifurcation structure of a four-dimensional Lorenz-like system with a wild chaotic attractor. Nonlinearity, 39 065010
Patiño-Echeverría, Krauskopf & Osinga (2026) Bifurcations of symmetric periodic orbits in a four-dimensional Lorenz-like system and their relation to wild chaos. Preprint, University of Auckland

PhD thesis

My thesis, “Transitions to Wild Chaos in a Four-Dimensional Lorenz-like Vector Field” (University of Auckland, 2026), studies how high-dimensional ODEs can produce robust chaotic behaviour, and how global bifurcations organise that behaviour in parameter space. Supervised by Professors Hinke Osinga and Bernd Krauskopf.

Posters and research snapshots: Figshare profile

Master’s thesis

Before my PhD, I completed a Master’s thesis in higher-education, “Del triángulo didáctico al grafo completo K4: nuevas aristas en los procesos de enseñanza-aprendizaje en la era tecnológica” (From the Didactic Triangle to the K4 Complete Graph: New Connections in Teaching and Learning in the Digital Age). It proposes a topological reinterpretation of the classic teacher–knowledge–student triangle as a complete graph K4, showing how digital tools add a fourth node to the teaching–learning relationship, illustrated with examples from university mathematics teaching.

Thesis available in Spanish (PDF)

3 Minutes thesis

Previous research

Summer Research Scholarship, Victoria University of Wellington Worked with Brendan Harding on fluid dynamics — specifically bifurcation phenomena related to inertial particle focusing and separation in spiral-duct flows.
Honours project, Victoria University of Wellington Supervised by Mark McGuinness. Investigated synchronisation in coupled oscillators.

Software

MAUTOLAB

A MATLAB toolkit for reading, parsing, and visualising output files produced by AUTO-07p — the numerical continuation software used throughout my PhD research.

AUTO produces three output file types per run (b.*, d.*, s.*), each in a compact but non-trivial plain-text format. MAUTOLAB provides a clean, MATLAB-native interface to all three, with both a programmatic API and interactive GUI apps for exploring bifurcation diagrams, solution trajectories, and eigenvalue/Floquet multiplier spectra.

View on GitHub

Additional project

Before starting my PhD, I founded and ran an online teaching initiative, Ingooz (2018–2020), that connected university students with tutors across Latin America.