Dr Andrus Allan Giraldo Munoz

PhD in Mathematics, The University of Auckland

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Research Fellow

Biography

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)

As of 29 October 2020 there will be no automatic updating of 'selected publications and creative works' from Research Outputs. Please continue to keep your Research Outputs profile up to date.
  • 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

Contact details

Primary office location

SCIENCE CENTRE 303 - Bldg 303
Level 2, Room 227
38 PRINCES ST
AUCKLAND CENTRAL
AUCKLAND 1010
New Zealand

Web links