Dr Andrus Allan Giraldo Munoz
PhD in Mathematics, The University of Auckland
See my homepage for up-to-date information.
Research | Current
- Global bifurcations theory of vector fields
- Numerical continuation techniques
- Compactification techniques applied to vector fields
- Nonlinear optics
- Semiclassical analysis of quantum optical systems
I am a mathematician specialising in Dynamical Systems. My research focuses on global bifurcations, and the application of state-of-the-art computational techniques for their detection and for understanding their overall behaviour. My research aims to connect theoretical results in the area of dynamical systems with physical phenomena for the purpose of understanding their qualitative behaviour.
Currently, I am studying and characterising dynamical phenomena that arises in different optical devices, e.g., photonic crystal nanocavities, fibre ring resonators; and in the semiclassical approximation of different quantum optical models.
Additionally, I am also developing and applying novel formulations for the continuation of two-point boundary value problems in the pursue of connecting known results in ODEs to PDEs, and delay differential equations.
Teaching | Current
MATHS 765: Mathematical Modelling -- Semester 2, 2021
Selected publications and creative works (Research Outputs)
- Stitely, K. C., Giraldo Munoz, A., Krauskopf, B., & Parkins, A. S. (2020). Nonlinear semiclassical dynamics of the unbalanced, open Dicke model. Physical Review Research, 2 (3), 033131-1-033131-18. 10.1103/PhysRevResearch.2.033131
Other University of Auckland co-authors: Kevin Stitely, Scott Parkins
- Giraldo, A., Krauskopf, B., Broderick, N. G. R., Levenson, J. A., & Yacomotti, A. M. (2020). The driven-dissipative Bose-Hubbard dimer: Phase diagram and chaos. New Journal of Physics, 22 (4).10.1088/1367-2630/ab7539
Other University of Auckland co-authors: Bernd Krauskopf
- Giraldo, A., Krauskopf, B., & Osinga, H. M. (2018). Cascades of Global Bifurcations and Chaos near a Homoclinic Flip Bifurcation: A Case Study. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, 17 (4), 2784-2829. 10.1137/17M1149675
Other University of Auckland co-authors: Bernd Krauskopf, Hinke Osinga