Personal webpage: bastiaansen.github.io

Mathematical Modeling of Climate and Ecosystem Dynamics

I am an Assistant Professor at the Mathematical Institute and the Institute for Marine and Atmospheric Research Utrecht (IMAU) at Utrecht University. My research sits at the intersection of Applied Mathematics, Climate Dynamics, and Ecology, focusing on the mathematical modeling of complex environmental and climate systems.

My work is fundamentally concerned with system stability and the potential for abrupt shifts—a concept often referred to as Tipping points. I use rigorous mathematical techniques, particularly from Dynamical Systems, to investigate these critical transitions in Earth system components. This includes analyzing phenomena like the potential collapse of the Atlantic Meridional Overturning Circulation or critical transitions in ecosystems. A major goal of this research is to understand how these systems maintain or evade catastrophic tipping, often through complex mechanisms like spatial pattern formation. For example, my PhD research focused heavily on the behavior of self-organized vegetation patterns in dryland ecosystems, utilizing advanced tools like asymptotic analysis, including geometric singular perturbation theory, numerical continuation and forward time integration to study how these patterns form and what they reveal about ecosystem resilience.

I also explore how ecosystems and climate (sub)systems change dynamically, and react to imposed forcing - for instance by studying the transient state-dependency of climate feedbacks and by applying mathematical and statistical methods to estimate crucial metrics, such as Equilibrium Climate Sensitivity.

Furthermore, I specialize in analyzing spatially extended systems, employing reaction-diffusion-advection models to understand how geographical and spatial effects can influence system stability, and how these mathematical models/systems in general work. In particular, I also study the effects of spatial heterogeneity of parameters on the dynamics of spatial patterns in these systems.

Some key words: Tipping Points, Pattern Formation, Asymptotic Analysis, Response Theory, Climate Sensitivity, Climate Dynamics, Dynamical Systems, Mathematical Modelling, Bifurcation Theory, Differential Equations, Climate Change, Nonlinear Dynamics, Singular Perturbation Theory, Matched Asymptotics, Spatial Patterns, Complex Systems, Ecosystem Dynamics, Resilience, Fast-Slow dynamics

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