Hi, I am Wei Hao Tey, a Malaysian and enjoying life as an early career researcher in applied mathematics. I am currently working as a Research Associate at Imperial College London. I enjoy exploring the wonders of the world, one of them was visiting The Isle of Skye (as you can see in the picture and my beaming smile). My favourite things to do are mountain climbing, piano and simulating dynamical systems (hence the animation included below). 

I graduated with a Ph.D. in Mathematics at Imperial College London, with a thesis titled 'On Minimal Invariant Sets of Certain Dynamical Systems: A Boundary Map Approach'.

Research

My main research interests are Dynamical Systems and Numerical Methods. Specifically, my current research focus is on random dynamical systems with bounded noise and their potential application in the prevention of brain diseases. The theories of Random Dynamical Systems have been popular among theoretical and applied mathematicians due to the involvement of probability and statistical theories, and their applications to a wide variety of natural processes which intrinsically possess uncertainties and errors. Most research focuses on unbounded noise which allows researchers to utilize tools in probability theory which was well established. However, in most natural processes, the uncertainties are bounded at least on a finite time scale. The model of bounded noise, with possibly bounded transient objects, unlocked the rich and deep knowledge of geometry and topology. 

In my Ph.D., I explored one of the tools to examine random dynamical systems with bounded noise - Set-Valued Dynamical Systems. Instead of focusing on each realization of noise in a random dynamical system, a set-valued approach where all possible trajectories are incorporated in a set-valued dynamical system. Then, by focusing on the boundary of the minimal invariant set, we reduce the infinite-dimensional problem to a finite-dimensional one. This resulted in the detection of sudden changes of these sets which are called topological bifurcations. We hope that this will allow us to have more theoretical control over critical transitions of complex systems, including the dynamics in the brain.

Simulations (Random Dynamical Systems with bounded noise)

[1] J. S. W. Lamb, M. Rasmussen, and C. Rodrigues, Topological bifurcations of minimal invariant sets for set-valued dynamical systems, Proceedings of the American Mathematical Society 143 (2015), no. 9, 3927–3937.

[2] K. Kourliouros, J. S. W. Lamb, M. Rasmussen, W. H. Tey, K. Timperi, and D. Turaev, Persistence of minimal invariant sets for certain set-valued dynamical systems: a boundary mapping approach, arXiv preprint arXiv:2303.01895 (2023).

[3] M. Dellnitz, G. Froyland, and O. Junge, The algorithms behind GAIO — Set oriented numerical methods for dynamical systems, Ergodic theory, analysis, and efficient simulation of dynamical systems, 2001, pp. 145–174.

[4] W. H. Tey, On minimal invariant sets of certain set-valued dynamical systems: a boundary map approach, Ph.D. Thesis, 2022.

[5] J.S.W. Lamb, M. Rasmussen, and W.H. Tey, Attractors of Linear Maps with Bounded Noise, arXiv preprint arXiv:2310.03437 (2023).