My research interest lies in applications of dynamical systems, more specifically, the study of nonlinear ODEs to model complex systems. Of particular interest is the Lorenz system, well-known for the so-called “butterfly effect”. Broadly, I am open to new ideas for applying dynamical systems to model real world scenarios.

My PhD project was concerned with deriving and exploring chaotic properties of new high-dimensional extensions of the Lorenz system, viewed as closer approximations of the Boussinesq fluid model for Rayleigh-Benard convection. Beyond the initial motivation for considering additional physical contexts under specific scenarios such as the presence of vertical gradient in scalar concentrations as in atmospheric aerosols or ocean water salinity, this project evolved into a quest to answer more fundamental questions about the chaotic nature of weather and fluid systems, leading to the derivation of a generalized high-dimensional Lorenz systems capable of furnishing an ODE system that represents a fluid system with arbitrarily high harmonic orders. Some interesting phenomena discovered along the way include a novel type of chaotic attractor, coexisting attractors, and synchronization of chaos, which led to some immediate applications in different fields such as image encryption technology and data assimilation in the context of numerical weather prediction. My ongoing research explores how different network configurations could change the synchronization properties, with certain configurations more prone to rare catastrophic events than others.

As a member of the Mathematics Public Health (MfPH) network at The Fields Institute, I had the opportunity to work on agent-based models for epidemic curves of a rapidly spreading infectious disease such as COVID-19. I focused on developing co-circulation models having two or more viral strains, utilizing both the traditional ODE-based approach (SIR) and the agent-based modeling (ABM) approach. My ongoing research in this area is focused on exploring how the infection network heterogeneity affects the epidemic curves and whether these effects can better be simulated using ABMs rather than ODEs.