Projects

PhD research
Wild chaos, global bifurcations, invariant manifolds, and numerical continuation in a four-dimensional Lorenz-like system.

Publications

Preprints

Patiño-Echeverría, Krauskopf & Osinga (2025) Global bifurcation structure of a four-dimensional Lorenz-like system with a wild chaotic attractor. 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

Animated phase-space projection from the 4D Lorenz-like system.

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.

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.